Smith was designated for assignment by the Twins on Wednesday, Do-Hyoung Park of MLB.com reports.
Smith was reinstated from the injured list in mid-July and posted a 13.50 ERA and 1.93 WHIP in 4.2 innings over six appearances following his return. He'll be cast off the 40-man roster after Caleb Thielbar (hamstring) was reinstated from the 15-day IL on Wednesday.