Unchosen in the Major League draft, Smith was selected in the first round of the independent Frontier League's draft by the Lake Erie Crushers. In 2011, Smith played for the Traverse City Beach Bums and Washington Wild Things of the Frontier League, as well as the White Sands PupFish of the Pecos League. In 13 combined appearances, Smith pitched to a 4–2 win–loss record, 3.64 earned run average, and 54 strikeouts in 59 innings pitched. In the offseason, Smith played for the Brisbane Bandits of the Australian Baseball League, where he posted a 3–3 record, 2.31 ERA, and 65 strikeouts in 50 innings. In 2013, Smith signed a minor league contract with the New York Yankees, but did not play that year due to a stress fracture in his forearm. In 2014, he was assigned to their Class-A affiliate, the Charleston RiverDogs. He was later promoted to the Advanced-ATampa Yankees, and in 32 total relief appearances, posted a 1–2 record, 2.98 ERA, and 49 strikeouts in 51 innings. Smith began the 2015 season with Tampa, and in May earned a promotion to the Double-ATrenton Thunder. At the end of May he was sent back to Tampa, and in late July Smith was released by the Yankees organization. Smith signed a minor league contract with the Toronto Blue Jays and played with the Advanced-A Dunedin Blue Jays and Double-A New Hampshire Fisher Cats. Smith made 31 total relief appearances in 2015, and pitched to a 4–2 record, 2.05 ERA, and 57 strikeouts in 52 innings. In the offseason, he played for the Gigantes de Carolina of the Liga de Béisbol Profesional Roberto Clemente. Smith was assigned to New Hampshire to open the 2016 minor league season, and earned a late-season promotion to the Triple-ABuffalo Bisons. He recorded a stellar campaign, making 47 appearances and posting a 1–3 record, 1.93 ERA, 76 strikeouts, and 15 saves in 60 innings.
On December 21, 2017, Smith signed a minor league contract with the Washington Nationals. He elected free agency on November 2, 2018.
Detroit Tigers
On December 13, 2018, Smith signed a minor league contract with the Detroit Tigers. Early in spring training, Smith suffered a torn ulnar collateral ligament in his right elbow. Smith was released by the Tigers on March 5, 2019, after the season ending injury. Smith re-signed with the Tigers on a minor league deal on February 7, 2020.