The dismissal comes after both players were arrested on drug charges in the last few months.
Coach Kevin Sumlin says: ''These two individuals have failed to meet the high expectations and standards that we have for our football players and as representatives of this university. These two players have exhibited a pattern of behavior that we will not tolerate at Texas A&M.''
Claiborne was named to the SEC All-Freshman team after piling up 89 tackles, including seven for losses last season. He started nine games and forced two fumbles.
Golden appeared in 11 games as a freshman last season and had 30 tackles and three tackles for losses.