Also on Wednesday, Cleveland lost left-handed reliever Scott Maine, who was claimed on outright waivers by the Blue Jays.
Rottino, 32, appeared in 18 games for the Indians last season. He collected three hits in 28 at-bats (.107 average) while spending time at left field, right field and catcher. The Tribe selected him off waivers from the Mets in late June. He hit .182 in 18 contests for New York during the 2012 campaign.
Slowey, sidelined for much of the year with a stress fracture in his rib cage, spent the entire season with the Clippers. The Indians acquired the right-hander from the Rockies last January. He is expected to play for Azucareros del Estes in the Dominican Winter League this offseason.
The Indians selected Maine off waivers from the Cubs on Aug. 29. The southpaw surrendered seven runs on 13 hits in six innings for the Tribe.
Cleveland's 40-man roster now stands at 34 players, with pitchers Carlos Carrasco, Josh Tomlin and Rafael Perez on the 60-day disabled list.