"This season is just getting started, and we have an opportunity to do something special with this team and program," Bohn wrote in a statement that announced his decision.
Bohn named associate head coach Donte Williams, in his second year on USC's staff, as the interim coach.
"Clay is one of the finest human beings I have met in this industry, and he has been a tremendous role model and mentor to our young men," wrote Bohn, who arrived from Cincinnati in 2019.
