Criswell was optioned to Triple-A Durham on Thursday, Marc Topkin of the Tampa Bay Times reports.
Criswell went 3.1 scoreless innings in a bulk relief role in Wednesday's win over the Twins, and his reward is a trip back to the minors. He's being replaced on the 26-man active roster by Yonny Chirinos, who was called up from Triple-A to start Thursday's series finale with Minnesota.