The Orioles also brought back pitcher Wei-Yin Chen to start Sunday against New York at Yankee Stadium. The left-hander is 7-7 with a 3.76 ERA, and the Orioles sent him to their Gulf Coast affiliate last week to create roster space.
Teagarden and outfielder Eric Thames were designated for assignment.
The 29-year-old Teagarden hit .167 with two home runs and five RBIs in 23 games for Baltimore. Thames was acquired from Seattle on June 30 and was in the minors.
Clevenger was obtained on July 2 from the Chicago Cubs in a multiplayer trade. He hit .199 with one homer and 16 RBIs for the Cubs.
The 32-year-old Snyder hit .118 in six games for Baltimore this year. He also has played for Arizona, Pittsburgh and Houston.