Mamuchashvili entered the Saburtalo football school at age 7.[1]
He made a debut for the senior team in a 4–1 win against Kolkheti Khobi on 31 August 2013 in the 2nd division. Four years later, he scored his first Erovnuli Liga goal in a 4–1 away victory over Dinamo Tbilisi.[2]
The next summer he ended his fourteen-year tenure at Saburtalo and moved to Liga 2 side Dinamo Batumi on a two-year deal, later extended for another two years.[3]
Mamuchashvili became a key player at the new club. In the first season, he featured in all remaining 19 games and helped the team to seal an immediate promotion back to the top tier. In 2021, he netted in each of the three rounds of the 2021–22 UEFA Europa Conference League campaign.[4] Later the same year, Dinamo Batumi won the champion's title with Mamuchashvili taking part in all games, except for one, and scoring nine goals.[5]
In 2023, Mamuchashvili contributed with 12 goals to Dinamo's another league triumph. At the end of the year, he received an individual recognition by being named in Team of the Season.[6]
Mamuchashvili made 24 appearances in all competitions the next year, becoming the team's top scorer with eight goals by early August. In this summer break, the player opted to leave Dinamo after a seven year-long spell.[7]
Mamuchashvili represented Georgia in all youth national teams. He made a debut for the senior team on 5 September 2021 in a World Cup qualifier against Spain, a 0–4 away loss. He started the game and played the whole match.[10]