The Detroit Tigers selected Smith in the third round of the 2015 Major League Baseball draft.[3] He signed with Detroit for $575,800[4] and was assigned to the GCL Tigers. After one appearance in the GCL, Smith was promoted to the Connecticut Tigers. He was promoted to the West Michigan Whitecaps in August and he finished the season there. In 31 relief innings pitched between the three clubs, Smith was 3-0 with a 0.29 ERA. In 2016, he returned to West Michigan and spent the whole season there, going 1-2 with a 2.96 ERA in 35 relief appearances.[5] He began 2017 with the Lakeland Flying Tigers.
On July 27, 2017, the Rays traded Smith to the New York Mets in exchange for Lucas Duda.[7] The Mets assigned him to the Binghamton Rumble Ponies and he finished the season there. In 42 relief appearances between Lakeland, Charlotte, Durham, Montgomery, and Binghamton, Smith pitched to a 4-4 record with a 1.65 ERA and 0.90 WHIP.[8] He began 2018 with Binghamton and was promoted to the Las Vegas 51s after two games.
The Mets promoted Smith to the major leagues on June 22, 2018.[9] He made his major league debut the next night at Citi Field against the Los Angeles Dodgers, pitching one scoreless inning in relief as the Dodgers defeated New York 8-3. He finished his 2018 season with the Mets, going 1-1 with a 3.54 ERA in 27 relief appearances. Smith underwent Tommy John surgery during 2019 spring training, forcing him to miss the year.[10]
Smith returned to game action in 2020, appearing in eight games for the Mets, registering a 6.43 ERA with seven strikeouts in as many innings pitched.[11] In 2021, although he missed time due to injury, Smith still made thirty relief appearances for the Mets, going 3-1 with a 2.40 ERA and 41 strikeouts over 41+1⁄3 innings.[12]
On April 29, 2022, Smith pitched in relief in a combined no-hitter against the Philadelphia Phillies, pitching 1+1⁄3 innings.[13] He made 44 appearances for the Mets in 2022, compiling a 3.33 ERA with 53 strikeouts across 46 innings of work.
Smith earned his first major league save in a game against the Washington Nationals, pitching +1⁄3 inning, on May 12, 2023.[14] On June 13, Smith was ejected upon entering a game against the New York Yankees after a sticky-substance check.[15] He was suspended 10 games and fined by MLB the following day.[16] Smith made 62 relief outings for New York in 2023, registering a 4–6 record and 4.15 ERA with 60 strikeouts and 3 saves across 56+1⁄3 innings pitched.
Smith began the 2024 campaign as part of the Mets' bullpen, recording a 3.06 ERA with 23 strikeouts and 2 saves in 19 games. On July 13, 2024, Smith underwent season-ending Tommy John surgery to repair his ulnar collateral ligament and would likely be out until 2026.[17]