Cleveland Indians Mujica originally signed with the
Indians as an undrafted
free agent on October 22, 2001. He quickly became one of the top pitching prospects in the Cleveland organization. Mujica began his career as a starter with San Felipe, the
Burlington Royals, and
Lake County Captains in 2002, 2003, and 2004. On June 21, , Mujica made his major league debut with Cleveland. He pitched scoreless innings, allowing three hits while striking out one batter. Mujica did not surrender an earned run in 2006 until his fourth appearance with the Indians, on July 14, a streak of consecutive innings (19 for Akron, for Buffalo and for Cleveland). Mujica was awarded the win in the first ever regular season game at
Citi Field against the
New York Mets on April 13. On May 23, he earned his first career
save in a 3–1 win over the
Chicago Cubs. Mujica spent the entire 2009 season with the Padres, posting a 3–5 record, two saves, and a 3.94 ERA and 76 strikeouts in 67 relief appearances. He pitched innings, allowing 101 hits and striking out 76 batters. Mujica appeared in 67 games in 2011, finishing 9–6 with 63 strikeouts and an ERA of 2.96. He was activated on July 18. Mujica made 41 appearances for the Marlins in 2012, going 0–3 with two saves and a 4.38 ERA. He was used primarily in the seventh inning of games for the team. In 29 relief appearances, Mujica recorded an excellent 1.03 ERA while striking out 21 batters in innings pitched. In 2013, when Cardinals closer
Jason 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 selection of his career. He was not called on to pitch, however. Mujica began to struggle due to lingering shoulder problems near the end of the season, and he posted a 11.05 ERA in September, resulting in his removal from the closer role. Mujica finished the season 2–1 with 37 saves and a 2.78 ERA in 65 relief appearances.
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. Mujica finished the 2014 season with a 2–4 record, eight saves and a 3.90 ERA in 64 appearances.
Oakland Athletics On May 9, 2015, Mujica was traded to the
Oakland Athletics in exchange for a
player to be named later or cash. In 38 relief appearances with Oakland, he finished 2–4 with one save and a 4.81 ERA. 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 0–3 record with 23 saves and an ERA of 3.69 in 39 innings with the Triple–A
Lehigh Valley IronPigs. He was released on August 10.
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 56 innings. He cleared waivers and was sent outright to Triple-A Toledo on August 15. He elected free agency on October 3.
St. Louis Cardinals (second stint) On January 31, 2018, Mujica signed a minor league contract to return to the
St. Louis Cardinals. He made 48 appearances for the Triple–A
Memphis Redbirds, going 3–2 while logging a 3.68 ERA with 35 strikeouts and 13 saves across innings pitched. ==Pitching style==