For his performance in the film, My Six Convicts (1952), Mitchell won the Golden Globe Award for Best Supporting Actor – Motion Picture. He is also known for his role as Col. Rufus Plummer in Billy Wilder's A Foreign Affair (1948), as Gregory Peck's commanding officer in the war drama Twelve O'Clock High (1949), and as the fictional movie mogul R. F. Simpson in the musical comedy Singin' in the Rain (1952).