Stitt was born in Detroit, Michigan and studied at Albion College to become a priest before receiving his BA from the University of Michigan and MFA from the Yale School of Drama. At Michigan, he studied playwriting with Kenneth Thorpe Rowe.
As a writer, Stitt is best known for his play,The Runner Stumbles, named best Broadway Play of 1976 in the annual Best Plays book. The film version of his screenplay was directed by Stanley Kramer with Dick Van Dyke, Kathleen Quinlan, Beau Bridges, Ray Bolger and Tammy Grimes.
A long-time member of the Circle Repertory Company, his plays produced there include, The Runner Stumbles with William Hurt, Back in the Race and Labor Day, which he wrote and directed for Christopher Reeve.
Stitt has written teleplays and mini-series for all the networks. His CBS television movie, The Gentleman Bandit, was the most-watched film of the season, and Long Shadow, for American Playhouse was nominated in 1996 for an International Emmy as Best Teleplay. His articles on theatre and travel have appeared in The New York Times and ''Horizon Magazine'.
Stitt has worked as a producer and in various administrative capacities at such theatres as American Shakespeare Festival, Long Wharf Theatre, American Place Theatre and Circle Repertory Company. At the Circle Repertory Company he founded the play development program and served as a dramaturg with such writers as Bill C. Davis, Albert Innaurato, Arthur Kopit, David Mamet, Lanford Wilson and Paul Zindel. For two years, he served as Executive Director of Circle Repertory Company producing premiere productions featuring artists Stephen Dietz, Laurence Fishburne, Kevin Heelan, Kikue Tashiro, Austin Pendleton, Heavy D, Olympia Dukakis, Rita Moreno, Fritz Weaver and Louis Zorich.
Stitt was chairman of the playwriting program at the Yale School of Drama for four years. He also taught dramatic writing at Princeton University, University of Michigan and at New York University. He was awarded a university chair and is now the Raymond W. Smith Professor of Dramatic Writing at Carnegie Mellon University.
Among his recent productions are Places We've Lived for the Pittsburgh New Plays Festival in June 2005. His libretto, co-written with choreographer Terrence Orr, for The Nutcracker continues in repertory at the Pittsburgh Ballet Theatre.
For several years, he served as an Adjudicator for the Ohio University Playwrights Festival and served as a mentor for Ensemble Studio Theater's Next Step Program. He frequently teaches workshops and adjudicates new plays for Oakland, Michigan's Heartlande Theatre. He is a member of the Dramatists Guild, Writers Guild of America, Author's League of America, P.E.N., the Eugene O'Neill Society and the National Academy of Television Arts and Sciences.