Motte was injured and set-up man Mitchell Boggs lost his effectiveness, Mujica became the new closer (around mid-April) and began collecting saves in his new role. On July 14, 2013, it was confirmed that Mujica would replace fellow Cardinal Adam Wainwright in the 2013 All Star Game, who had pitched two nights before against the Chicago Cubs. It was Mujica's first All Star Game appearance of his career. He was not called on to pitch, however. He became a free agent after the 2013 World Series on October 31, 2013. Boston Red Sox On December 5, 2013, Mujica agreed to a two-year, $9.5 million contract with the Boston Red Sox, pending the completion of a physical examination. The contract became official on December 7. He was designated for assignment by Boston on May 8, 2015. Oakland Athletics On May 9, 2015, he was traded to the Oakland Athletics in exchange for a player to be named later or cash. Philadelphia Phillies On December 17, 2015, Mujica signed a minor league contract with the Philadelphia Phillies, receiving an invitation to spring training. He was released on March 29, 2016 and re-signed a day later. He was released on July 14 after requesting his release. He posted an ERA of 3.69 in 39 innings at the AAA level. Kansas City Royals On July 15, 2016, Mujica signed a minor league contract with the Kansas City Royals. He was released on August 10. Minnesota Twins On August 19, 2016, Mujica signed a minor league contract with the Minnesota Twins. On August 20, he was assigned to AAA Rochester. Detroit Tigers On January 10, 2017, Mujica signed a minor league contract with the Detroit Tigers that included an invitation to spring training. On August 3, he was recalled from the Toledo Mud Hens by Detroit to replace Michael Fulmer, who was placed on the 10-day disabled list. At the time of his recall, Mujica had appeared in 46 games for Toledo, posting a 1–1 record, 12 saves, and a 2.35 ERA in 46 innings. On August 13, 2017, the Tigers designated Mujica for assignment. Second stint in St. Louis On January 31, 2018, Mujica signed a minor league contract to return to the St. Louis Cardinals. He became a free agent after the season ended. Leones de Yucatan Mujica spent the 2019 season with the Leones de Yucatan of the Mexican Baseball League and