Graham was designated for assignment Friday, LaVelle Neal of the Minneapolis Star Tribune reports.
The Twins brought Darin Mastroianni and Juan Centeno up from Triple-A, so two spots on the 40-man roster needed to be cleared for them. Graham was not good in his lone appearance out of the Twins bullpen, giving up two runs on three hits and a walk in 1.2 innings of work, which made him more expendable to the organization. He'll head back to the minors and act as organizational pitching depth going forward.