The trio had been designated for assignment on Nov. 18, and the Yankees announced their release Monday.
Eovaldi will be sidelined next season as he recovers from Aug. 19 surgery to repair a torn flexor tendon and partially torn ulnar collateral ligament in his right elbow. Acquired from the Miami Marlins in a December 2014 trade, Eovaldi was 9-8 with a 4.76 ERA this year.
He made $5.6 million, would have been eligible for salary arbitration and would have become eligible for free agency, anyway, after the 2017 season.
Rumbelow, a seventh-round draft pick of the Yankees in 2013, tore a ligament in his right elbow while pitching for Triple-A Scranton in his season debut on April 10, an injury that required Tommy John surgery. Now 25, he was 1-1 with a 4.02 ERA in 17 relief appearances in 2015.
Mantiply was claimed off waivers from Detroit on Nov. 8.