Blevins will have surgery next week and could be out for the rest of the season, the team said.
O’Flaherty, 30, was designated for assignment by the A’s on Aug. 1. The Walla Walla, Washington native was 1-2 with a 5.91 ERA in 25 games for Oakland this season.
The Atlanta Braves completed a three-game sweep over the Mets on Sunday. Atlanta won in extra innings 3-2.