Gruden reportedly made the decision to release King, which shaves $2.9 million from the salary cap.
It is not clear what those personality issues were but former coach Jack Del Rio said in 2016 that he was frustrated with King after he was assessed 15-yard personal foul penalties in consecutive games.
A second-team All-Pro selection in 2016, King finished first in Pro Bowl fan voting last year, although he was never selected for that all-star game.
King ranked sixth in the NFL in punting average last season at 47.4 yards per kick.
The Raiders signed King to a five-year, $16.5 million contract extension a year ago.
King, signed by Oakland as an undrafted free agent in 2012, spent six years with the Raiders. He played 80 games, punting 426 times for a 46.8-yard average. He put 156 punts inside the 20-yard line.
The Raiders might go with Colby Wadman as their punter. The Raiders signed Wadman in March but he has never punted in an NFL game.