Warburton was born in 1911, in San Diego, California, to Margaret Warburton where he attended San Diego High School, and won the California high school 440-yard dash in 1930. He brought his speed to the USC Trojans football team, and was chosen as an All-American quarterback in 1933. Warburton was the quarterback during a winning streak that lasted for 27 games, which remained unsurpassed at USC until 1980.
Deciding to retire from football, he turned to film work and began as an assistant film editor for MGM where would contribute to films, like Air Raid Wardens, Neptune's Daughter, and Crazylegs, where Warburton was nominated an Academy Award for Best Film Editing. He also worked as an editor on the hit show, The Adventures of Ozzie and Harriett.
In 1956, Warburton began working for Disney where he remained for the rest of his career. During this time, he would collaborate with director Robert Stevenson in films, like The Absent-Minded Professor, The Misadventures of Merlin Jones, The Monkey's Uncle, That Darn Cat, The Love Bug, The Happiest Millionaire, Bedknobs and Broomsticks, Herbie Rides Again, and Mary Poppins, where he won his only Academy Award as well as the American Cinema Editors Eddie Award.
Cotton was elected to the College Football Hall of Fame in 1975.