From 1808 to 1811, Joseph attended secondary school in Stamford, Connecticut, then attended Yale from 1811 to 1815. His classmates included John M. Clayton, who became Secretary of State, and Truman Smith, who became United States Senator for Connecticut. After graduation, Joseph continued at Yale as a tutor and secretary to the first President Dwight, while studying for the ministry under Professors Fitch and Goodrich at what subsequently became the Yale Divinity School. During this time, he was also rector of the Hopkins Grammar School, and published several poems and other articles in the Microscope of New Haven. During his time at Yale, Joseph became interested in the legacy of his predecessor and cousin William Wickham (Yale, 1753). While at Yale, William had founded the Linonian Society, a literary and debating society that dominated social life at Yale until the Civil War. William went on to become a very successful attorney in Orange County, NY, where his son George Duncan Wickham was an influential businessman.

Joseph was licensed to preach by the New Haven West Association on January 2, 1821. That year, he began his ministerial career as a missionary to Long Island. He then spent a period in central New York on behalf of the Presbyterian Education Society. After a unplanned visit in 1822 to Oxford in Chenango County, NY, he was invited to take charge of the Presbyterian Church there, and at the dedication of a new house of worship, he was ordained to the ministry. In 1825, he moved to Westchester County, NY to manage for three years the Presbyterian churches in West Farms and New Rochelle.

Joseph was married on May 26, 1823, to Julia A. Porter, the only daughter of Jonathan E. Porter (Harvard, 1786), of New Haven, CT, and a niece of President Dwight. As small trim woman with keen black eyes, she died after a protracted illness in New York City on December 23, 1830 at age 38. He married again on December 28, 1831, to Amy Porter, third daughter of Col. Moses Porter, of Hadley, Massachusetts and Amy Colt, and a cousin of his first wife, who died October 29, 1832 at age 32. He was married a third time, on October 12, 1834, to Elizabeth Cooke Merwin, eldest daughter of the Rev. Samuel Merwin (Yale, 1802) of Wilton, CT, who survived him. Of his two children, a daughter by his first wife died in infancy (Mary Louisa Wickham, born November 7, 1827, died July 1828); and a daughter by his second wife survived him. (Emma Wickham, born October 21, 1832 in New Haven, Connecticut; she was raised by her stepmother Elizabeth, who found Emma difficult because she was the "pampered favorite of all her grandparents.")

In 1828, Joseph became one of the proprietors of Washington Institute, the most prominent boarding school in New York City. He remained there (eventually in sole charge) until November 1834, when the school was transferred to the care of his two brothers-in-law, Timothy Dwight Porter (Yale, 1816) and Theodore Woolsey Porter (Yale, 1819). Joseph was then installed pastor of the recently organized Presbyterian Church at Matteawan in the town of Fishkill, NY. During this time, he and Charles Bartlett ran the Highland Gymnasium at Fishkill Landing. After about a year in Fishkill, he spent two years among the churches of upstate New York and western Pennsylvania on behalf of the Presbyterian Education Society.

In December 1837, Joseph moved to Manchester, Vermont, to become headmaster of the Burr Seminary, a leading secondary school opened in 1833 that was later renamed the Burr and Burton Academy (see school). During his tenure, the school became firmly established and was Vermont's first coeducational secondary school. He remained connected with that institution for twenty-five years, except for three years (1853-1856), in the first of which he was Treasurer of Middlebury College and Acting Professor of Latin and Greek, while for the two following years he was connected with the Collegiate Institute in Poughkeepsie, NY. In 1856, he returned to lead Burr Seminary, then retired from his position in 1862, though continuing to serve as President of its Board of Trustees until his death. Burr and Burton Academy has established The Joseph Wickham Society, named for the school�s longest serving headmaster, to honor faculty and staff who have served for 25 years.

During his time in Manchester, Joseph and his wife Elizabeth were very active members of the First Congregational Church of Manchester, an association that lasted for 54 years. He became the unofficial associate pastor of that church and also taught a large Bible class for many years. Joseph was also chosen a member of the Board of Trustees of Middlebury College in 1840, and continued in that position until his death. That school conferred upon him the degree of D.D. in 1861. That same year, Yale College granted him the degree of S.T.D.

Joseph retired to Manchester, Vermont in 1862, where he lived for the next 29 years, until he died of old age on May 12, 1891, in his 95th year. (The average U.S. life expectancy when he was born was about 35 years). He remained physically fit and mentally alert until the end. He had been for five years the last survivor of his Yale class, and for three years the oldest graduate of the College, and the last surviving graduate under the elder President Dwight. The address at his funeral was given by the Rev. P.S. Pratt.

Joseph's wife Elizabeth died on February 22, 1901. Besides being an active member of the First Congregational Church of Manchester, she served as preceptress of Oxford Academy in Oxford, New York, from December 1832 to August 1834. In 1893, she published an 84-page biography of her husband called A Long and Well Spent Life: Recollections of Joseph Dresser Wickham. She also had a memorable article published in the Manchester Journal on February 12, 1869 called A Lost Family Found about her church's sexton, Cyrus Branch (aka John White), who had escaped from slavery in Virginia 33 years earlier and had not seen his family since, though he longed to do so. Branch, considered a model citizen in Manchester, was mum about his past and kept a loaded pistol with him at all times until the Civil War, due to a federal law that required the capture of all fugitive slaves, even those in Vermont. During his dramatic escape from Virginia, he was chased by dogs and shot twice.

Joseph's daughter Emma attended York Square Academy in New Haven in 1845-1846, and also attended Burr and Burton Seminary. During 1854-1855 she taught French and music at Oxford Academy, where her step-mother had been preceptress. In 1860, she was married to Rev. Alfred Cox Roe (1823-1901), a Presbyterian clergyman and educator, just like her father. In 1863, Alfred was ordained by the Presbyterian Church and appointed chaplain to the 83rd Regiment of New York Volunteers. In August of the following year, this regiment was annihilated during a Union victory at the Battle of Globe Tavern. He was re-commissioned in the 104th Regiment, in which he served until his discharge in July 1865. He was Eastern Secretary of the American Christian Commission in New York City from 1866-1869 and was pastor of a Presbyterian church in Lowell, Massachusetts from 1870-1871. He returned to New York state, serving Presbyterian congregations in Geneva 1871-1873, Galen 1873-1874, and Clyde 1875-1876. In 1877, he founded the Cornwall Collegiate Institute for Young Ladies at Cornwall on the Hudson. He also opened the Berkeley Institute in Brooklyn in 1883 and the New York Collegiate Institute of Harlem in 1888. Alfred retired in 1895, and he and Emma moved to Colony, Oklahoma in 1897 to be missionaries to Native Americans. They returned to the Wickham home in Manchester, Vermont in 1901, where Alfred died in September of that year, followed by Emma's death there in December 1906.

Emma and Alfred had three children together: Joseph Wickham Roe (1871-1960), Mary Wickham Roe (1863-1941) and Elizabeth Merwin Roe (1861-1943). Their son Joseph graduated from Yale's Sheffield Scientific School in 1895, worked for several manufacturing companies, then received a M.E. degree from Yale in 1907. He taught mechanical engineering and machine design at Sheffield Scientific School until 1917, when he was commissioned a major in the Aviation Section, Signal Reserve Corps of the Army. He returned to teaching in 1921 as professor and chairman of the Department of Industrial Engineering at New York University, from which he retired in 1937. He was a consultant for the Navy during World War II and was the author of numerous articles and books on engineering and management. His sister Mary Wickham Roe taught high school classes for several years, then became a missionary to Native Americans living in the United States and Latin America. She and her husband Walter adopted Henry Roe Cloud, an orphan from the Winnebago Reservation who became the first Native American to graduate from Yale and is considered the most important Indian leader of his generation. Among his accomplishments were conserving Indian lands, protecting the legal rights of Indians, and improving the educational systems of the reservations (see Mary, Walter and Henry (left)). Mary was killed in a car accident on June 17, 1941 while attending a mission conference in New Mexico. Her sister Elizabeth Merwin Roe served as Field Secretary for the Women's Board of Domestic Missions of the Reformed Church in America from 1903 to 1913. She was the author of In Camp and Tepee published in 1915, a book about the Indian mission activities supported by the Women's Board. Her daughter Elizabeth Page wrote the 1939 best seller The Tree of Liberty. The film rights were sold to Columbia Pictures for $55,000 and the resulting 1940 movie The Howards of Virginia, starring Cary Grant and Martha Scott, was nominated for two Oscars (see movie poster).

The Yale University Library keeps on file 27 boxes of items called the Wickham Family Papers that consist of correspondence, family papers, diaries, sermons, photographs, and other materials documenting the personal lives and professional careers of Joseph and his family. These were a gift of Joseph's descendants Marjorie Page Schauffler and Elizabeth Schauffler Lyman.