Vincent was suspended for spring practice for an unspecified violation of team rules.
Coach Tommy Bowden said in a news release Monday that Vincent would have been academically eligible to compete in the fall, but did not meet goals set by the team for the spring.
Vincent started 12 games last season and had 68 tackles and two sacks.
He would have been a fifth-year senior in the fall and will have to transfer to a Division II or Division III school to play this season.
Clemson also announced that wide receiver Jeff Ogren will transfer to another school. Ogren played in four games last year and had one reception for eight yards.