Additionally, the Twins reinstated right-hander Nick Blackburn (forearm surgery) and second baseman Alexi Casilla (right hamstring strain) from the 60-day disabled list. As a result of their roster moves, the Twins now have 38 players on their 40-man roster.
Rivera, 28, appeared in 45 games with the Twins, hitting .144 with a .211 on-base percentage and .202 slugging percentage. He homered once and drove in five runs.
Tolbert, 29, hit .198/.252/.266 with 11 RBIs and three stolen bases in 87 games while seeing time at second base, shortstop and third base.
Repko, 30, battled various injuries during the regular season, playing in 67 games and batting .226/.270/.286 with two homers and 11 RBIs.
Slama, meanwhile, made just two relief appearances with the Twins, tossing 2 1/3 scoreless innings. The 27-year-old, who saw his season end in early July with a strained muscle in his right elbow, posted a 2.92 ERA with 42 strikeouts and 16 walks in 37 innings with Triple-A Rochester.