The Mets selected Smith in the first round, with the eleventh overall selection, of the 2013 Major League Baseball draft. Rather than attend USC, he signed with the Mets for a $2.6 million signing bonus. The Mets assigned Smith to the Gulf Coast Mets of the Rookie-levelGulf Coast League, where he batted.287 with three home runs and 22 runs batted in in 48 games. He was subsequently promoted to the Kingsport Mets of the Rookie-level Appalachian League, where he recorded four doubles in six at bats. At season's end, Baseball America named Smith as the 4th best prospect in the GCL for 2013. He spent the entire 2014 season with the Savannah Sand Gnats of the Class ASouth Atlantic League. With just one home run, 44 RBIs and 77 strikeouts in 461 at bats, Smith fell way short of expectations. Smith got off to a slow start with the St. Lucie Mets of the Class A-AdvancedFlorida State League in 2015. He batted.143 with one double in his first sixteen games, and was 0-for-22 to start May. On May 12, Smith got his first extra base hit since Opening Day with a double against the Tampa Yankees. The 3-for-5 performance signaled a turn around for Smith, who compiled a sixteen-game hitting streak to raise his batting average to.260. For the month of June, Smith batted.352 with a FSL-leading 38 hits and 51 total bases. He also had the second most RBIs and fifth most runs scored to earn FSL Player of the Month honors. The hot hitting continued; Smith ended the season with a.305/.354/.417 slashline, and a career high six home runs. He led the league with 79 RBIs and 33 doubles on his way to being named FSL Player of the Year. After the season, he played for the Salt River Rafters of the Arizona Fall League. In 2016, Smith played for the Binghamton Mets of the Class AAEastern League, where he posted a.302 batting average with 14 home runs and 91 RBIs. He played in the 2016 All-Star Futures Game. The Mets assigned Smith to the Las Vegas 51s of the Class AAAPacific Coast League to start the 2017 season. The Mets promoted Smith to the major leagues on August 11, 2017 after Fernando Salas was designated for assignment. He made his debut that night against the Philadelphia Phillies at Citizens Bank Park, recording a single for his first off of Nick Pivetta. Smith hit his first home run off of Sonny Gray on August 15. He ended the 2017 season with a.198 batting average and nine home runs in 167 at bats for the Mets. In spring training in 2018, Smith was set to compete with Adrián González to be the Mets' starting first baseman, but he missed most of spring training due to a quadriceps injury. He began the season in Las Vegas, and was promoted on May 11 when Jay Bruce went on the paternity list and demoted when Bruce returned on May 14. Smith was promoted again on June 11 when the Mets released Adrián González. Smith was demoted again on July 20 after Yoenis Céspedes was activated from the disabled list. During spring training in 2019, Smith resumed using a continuous positive airway pressure machine. Smith had been diagnosed with sleep apnea in 2016 when, during a sleep study, he stopped breathing 90 times per hour—a doctor told him that 30 breathing stoppages per hour would have been considered a severe case. He and Mets general manager Brodie Van Wagenen credited the treatment with making him more alert and productive on the field that spring. Smith would return from the IL when making an appearance in the last game of the Mets regular season on September 29th. In his first at-bat back, he hit a three-run walk-off home run off Grant Dayton with the Mets down by two runs, leading the team to a 7–6 win in the bottom of the 11th inning over the Atlanta Braves.
Personal life
Smith's parents, Clay Smith and Yvette LaFleur, have seven children total. They lived separately while raising Dominic. His mother works in child care and his father is a dog trainer and groomer. Smith grew up a Los Angeles Angels fan.