The veteran nickel back was cut Tuesday, according to a tweet by his agent, Andrew Simms. The move came less than 24 hours after Sapp gave up the longest play in New England Patriots history on a pass from Tom Brady to Wes Welker.
Brady threw for a team-record 517 yards and four scores Monday night to help New England win 38-24.
The departure of Sapp, an eighth-year pro, leaves Nolan Carroll and rookie Jimmy Wilson as the Dolphins' backup cornerbacks. Starters Vontae Davis and Sean Smith were also beaten repeatedly by the Patriots.