The Cardinals optioned Suarez to Triple-A Memphis on Friday.
Suarez allowed three runs over two innings in each of his two appearances for St. Louis, and will now head back to the minors in order to right the ship. Though his 4.08 ERA and 1.48 WHIP in Triple-A aren't too impressive, Suarez could return to the Cards' bullpen later this season if the major-league club needs a fresh arm.