The Tigers announced Thursday they didn't offer Miner a contract, three days after they designated the right-hander for assignment.
Detroit has offered deals to Zumaya and Galarraga, both of whom were eligible for salary arbitration.
Miner didn't play last season and had surgery on his right elbow in May. He was 25-20 with a 4.24 ERA in 157 appearances, including 35 starts, in four seasons with the Tigers.
Zumaya's season ended in June when he broke his right elbow. He missed much of the previous three seasons because of shoulder and finger injuries. He helped the Tigers reach the World Series as a rookie in 2006 with a 1.94 ERA in 62 games.
Galarraga famously came close to a perfect game in June when umpire Jim Joyce ruled a runner safe at first base on what would've been the final out and then acknowledged after the game he made the wrong call. Galarraga finished the year 4-9 with a 4.49 ERA.