His first film as an assistant editor was The Wild Bunch (directed by Sam Peckinpah, 1969). Cox has had a notable collaboration with Clint Eastwood that commenced with the 1976 film The Outlaw Josey Wales, for which Cox was Ferris Webster's assistant. Cox and Webster were co-editors on The Gauntlet (1977) and on several more of Eastwood's subsequent films. Starting with Sudden Impact (1983), Cox became Eastwood's principal editor. Cox has been quoted as saying that, over their 30-year partnership, Eastwood has re-cut only a single scene that Cox put together. Gary D. Roach, who worked as Cox's assistant from the mid-1990s, has become Cox's co-editor on Eastwood's films since Letters from Iwo Jima (2006).
Cox won the 1992 Academy Award for Film Editing for Unforgiven. He has been elected as a member of the American Cinema Editors. On November 25, 2008, Clint Eastwood presented Cox the first Ignacy Paderewski Lifetime Achievement Award, which is named in honor of the piano virtuoso who called Paso Robles home, at the first Paso Robles Digital Film Festival. He received a nomination for the 2009 BAFTA Award for Best Editing for Changeling and for the 2015 Academy Award for Film Editing for American Sniper.