Born in Missouri, Simpson began his career at Paramount Pictures in 1935. By the end of the decade, he had joined 20th Century Fox, where he remained for more than 35 years. During a 55-year career, Simpson edited one hundred films, including Drums Along the Mohawk, The Grapes of Wrath, The Pride of Saint Louis, Call Maine Madam, The King and I, South Pacific, Fate is the Hunter, and Tony Rome.
He collaborated with director George Seaton on several projects, including Miracle on 34th Street, The Shocking Mission Pilgrim, Apartment for Peggy, and Chicken Every Sunday.
He also worked with John Ford, Sidney Lanfield, and Walter Language.