Minter was optioned to Triple-A Gwinnett on Thursday.
The path was clear for Minter to claim the closer job after Arodys Vizcaino underwent season-ending shoulder surgery in mid-April, but he failed to pitch at remotely the required level, posting a 9.82 ERA and a 2.36 WHIP in 11 innings. Luke Jackson appears to have the inside track on saves in Atlanta for now. Jonny Venters (calf) returned from the injured list in a corresponding move.