Robert Mitchell began his design career at Yale, where he studied with Donald Oenslager. He later assisted Jo Mielziner on the design of the Vivian Beaumont Theatre at Lincoln Center and 17 other theaters across the United States.

Off-Broadway credits include the English-language world premiere of Jean Genet's The Screens at the Brooklyn Academy of Music, as well as designs for Circle in the Square, The American Place Theatre, The Denver Center, and the Roundabout Theatre Company.

International design credits include many productions in England and Canada; the ballet La Peri for the Paris Opera; Medea starring Melina Mercouri and Oedipus Tyrannos in Greece. Oedipus, originally produced in the ancient theatre of Epidaurus became Greece's entry to the 1983 Europalia Festival in Brussels and to the Los Angeles Olympic Arts Festival in 1984.

He also designed concerts for David Bowie and Emerson, Lake, and Palmer.

Dance designs include The Lottery and L'Absence for The Harkness Ballet, Cantique des Cantiques for Les Grands Ballets Canadiens, and In Retrospect, Equinox, Under the Sun, American Rhapsody and The Veil for the Pennsylvania Ballet.

In 1970, Mr. Mitchell became the Director of Design and Theatre Technology at the Annenberg Center of the University of Pennsylvania.

In later years, Mr. Mitchell assisted dance companies with limited resources for scenic design. These included the National Dance Institute headed by Jacques D'Amboise, and the Sachiyo Ito Dance Company.

He also consulted on the design of many theatres, including Ford Center for the Performing Arts (now the Lyric) on Broadway.