On June 23, 1875, Mitchell was married to Mary Cadwalader (1835–1914), who was from one of Philadelphia's most prestigious families. She was a daughter of Thomas McCall Cadwalader and Maria Charlotte Gouverneur (niece of Elizabeth Kortright, who had married U.S. President James Monroe). The marriage "propelled him to one of the city's highest social circles and he became a trustee of the University of Pennsylvania the following year." Together, they were the parents of a daughter:

• Marie Gouverneur Cadwalader Mitchell (1876–1898), who died unmarried.