Mitre is 0-1 with a 3.27 ERA in 22 appearances for Milwaukee this season.
Braddock was on the disabled list because of a sleep disorder earlier this season. He rejoined the Brewers earlier this month but was sent to Nashville on June 15.
Gamel hit .241 with five home runs and 21 RBI in 145 at-bats with the Brewers over the previous three seasons. He has been hot for Nashville of late and could be used as a designated hitter for the Brewers' series against the Yankees in New York this week.