Mamukelashvili's older brother David introduced him to basketball at a young age, and Sandro grew up idolizing the Georgian player Zaza Pachulia.

In 2016, he moved to the United States to attend Montverde Academy, where he played alongside Toronto Raptors player RJ Barrett.

[4] On April 20, 2017, Mamukelashvili committed to playing college basketball for Seton Hall over offers from USC, South Carolina, and Vanderbilt.

[5] As a freshman, Mamukelashvili averaged 2.6 points, 1.9 rebounds and 0.5 blocks per game and helped the Pirates reach the second round of the NCAA Tournament.

[8] Following his sophomore season, Mamukelashvili worked with Pachulia at his Academy in Tbilisi to expand his game, adding a jump stop and improving his three-point shooting.

[10] On February 19, with his father Zurab in attendance for the first time in two years, Mamukelashvili scored 15 points and had six rebounds, hitting the game-winning shot on an inbounds pass with 0.6 seconds remaining in a 74–72 win over Butler.

After the season, he declared for the 2020 NBA draft but did not hire an agent, signaling high potential to return to Seton Hall for his senior campaign.

[14] Coming into his senior season, Mamukelashvili was named to the Preseason First Team All-Big East, and he was expected to help replace the graduated Myles Powell.

At the close of the season, he was named the Big East co-Player of the Year and won the Haggerty Award as the best player in the New York metropolitan area.

[22] On November 29, while playing with the Herd, Mamukelashvili posted 28 points, six rebounds, three assists, three blocks, and one steal in a win against the Windy City Bulls.

[26] On March 3, 2023, the San Antonio Spurs claimed Mamukelashvili off of waivers and converted his deal to a standard NBA contract.