Mitchell attended Columbia Grammar School from 1854 to 1857. He then went to Columbia College in 1857, graduating from there with a B.A. in 1861. He then went to Columbia Law School, but he left that year to serve in the American Civil War a volunteer field agent for the United States Sanitary Commission. He served in Richmond, Antietam, Port Hudson, and the Red River expedition. Afterwards, he finished his studies at Columbia Law School, graduating from there with an LL.B. in 1865. He was admitted to the bar later that year and practiced law. In 1880, he became a trustee of Columbia.