Frank is the only child of American painter, Eleanore Lockspeiser (1909–1986) and English musicologist and art critic, Edward Lockspeiser (1905–1973). During World War II Mary was sent to live in Brooklyn, New York with her maternal grandpartents, Gregory and Eugenie Weinstein. She studied modern dance with Martha Graham from 1945 to 1947 and was admitted to the High School for Music and Art in New York. In 1949 she transferred to the Professional Children's School where she majored in dance.