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.