Grissom made his professional debut with the Rookie-levelGulf Coast League Braves, batting .288 with three home runs and 23 RBIs over 44 games.[6] He did not play a minor league game in 2020 due to the cancellation of the season.[7] He began the 2021 season with the Augusta GreenJackets of the Low-A East,[8][9] and was promoted to the Rome Braves of the High-A East in September.[10][11] Over 87 games between the two teams, he slashed .319/.418/.464 with seven home runs, 43 RBIs, and 16 stolen bases.[12] Grissom returned to Rome to begin the 2022 season.[13] In mid-July, he was promoted to the Mississippi Braves of the Double-ASouthern League.[14][15] He recorded 91 at-bats in 22 games with Mississippi, hitting .363/.408/.516 prior to receiving a major league call-up.[16][17]
On August 10, 2022, the Braves selected Grissom's contract and promoted him to the major leagues following an injury to Orlando Arcia.[18] He made his MLB debut that night as Atlanta's starting second baseman at Fenway Park versus the Boston Red Sox, going 2-for-4 with a two-run home run over the Green Monster off of Darwinzon Hernández and a stolen base.[19][20] At age 21 and seven months, Grissom became the youngest player in either the American League or National League history to homer and steal a base in his major league debut.[17]
Following the departure of Dansby Swanson in free agency, Grissom entered the 2023 regular season with a opportunity to become the Braves' starting shortstop.[21][22] Grissom battled with Arcia and Braden Shewmake for the starting shortstop job during spring training. On March 20, Grissom and Shewmake were optioned to the Triple-A Gwinnett Stripers in favor of Arcia.[23]
On December 30, 2023, the Braves traded Grissom to the Boston Red Sox in exchange for Chris Sale and cash considerations.[24][25] During 2024 spring training, Grissom suffered a groin strain, delaying his availability for the start of the regular season.[26] On May 3, he was activated from the injured list and made his Red Sox debut.[27] On June 1, Grissom exited a game in the 2nd inning after grounding out and straining his hamstring.[28]