Stauffer was 1-0 with a 6.60 ERA in 15 innings season. He logged a 3.50 ERA in 61 1/3 innings last year with San Diego and the Twins signed him to a one-year, $2.2 million contract in the offseason.
"[I have] good things to say about Tim and what he did, how he came in here, how he handled himself," Twins manager Paul Molitor said. "It didn't work out particularly well and we'll wish him well. I'm sure he's going to land somewhere, somehow. I'm not sure how that's going to unfold in the next few days so we're going to move on to Michael.