Mitchell won Tony Awards for his work on Annie and Barnum and received Tony Award nominations for his designs for Trelawny of the Wells, Working, Can-Can, Foxfire, and The Boys of Winter. Among his other credits are La Cage aux Folles, Brighton Beach Memoirs and Biloxi Blues on Broadway, as well as numerous Off-Broadway productions, including the Obie Award-winning The Increased Difficulty of Concentration by Vaclav Havel.
He also designed for ballet and opera, contributing to productions at the New York City Ballet and New York City Opera; and he was responsible for production design on such films as Rich Kids, One Trick Pony, and My Dinner with Andre.
He is survived by a daughter and son.