Kelly was kicked off the team for conduct detrimental to the program, coach Dabo Swinney said in a statement.
"He has had a pattern of behavior that is not consistent with the values of our program," Swinney said, "I hope he will mature and grow from this and become the man and player I know he can be. I wish him nothing but the best in the future academically and athletically."
Kelly is the nephew of Buffalo Bills star Jim Kelly. The sophomore was expected to compete with senior Cole Stoudt and freshman Deshaun Watson to replace Tajh Boyd behind center this fall.
Kelly didn't come to Clemson quietly. At 6-foot-1 and 210 pounds, he was a highly sought recruit out of Buffalo, N.Y., choosing the Tigers over Alabama, Florida State, Michigan State and Purdue.
He taunted Stoudt, who has been a backup to Boyd all three years, on Twitter before he arrived, writing that "your on the bench for a reason! And i come soon! Just letting you know."
Kelly tore his ACL in the 2013 Clemson spring game, but came back to appear in five games in the fall. He completed 10 of 17 passes for 58 yards and ran 16 times for 117 yards, including a 38-yard touchdown run against Virginia.
Kelly threw two interceptions in last weekend's spring game, completing 10 of his 18 passed for 118 yards before being benched.