Stauffer has been on the disabled list twice this season with a strained right elbow. His second stint started on May 15.
It was the second time this week Stauffer has thrown off a mound. He'll now head to the Padres' Spring Training facility in Arizona where he'll throw two more bullpen sessions before appearing in games for the Padres' Arizona League affiliate sometime next week.
"No issues whatsoever," Stauffer said of his elbow. "I was able to throw and not worry about how it felt. Now it's just a matter of building up arm strength."
Stauffer, who has appeared in one game this season, is anxious to get back out on the mound in an actual game again.
"Being on the DL isn't a whole lot of fun," Stauffer said. "But now that I'm getting closer ... I'm anxious to get back and compete."
San Diego manager Bud Black said it would likely be another two and half to three weeks before Stauffer is ready to rejoin the Padres. It has yet to be determined, Black said, when Stauffer does join the team if it will be as a starter or reliever.
"He's in a good place mentally and physically," Black said.