Mamardashvili stands at 6 feet 6 inches (1.98 m) and is one of the tallest keepers in Europe's big five leagues. His rise from Georgia’s domestic leagues to the top level of Spanish football has been both rapid and impressive. Calm under pressure and difficult to beat, he’s earned a reputation for his strong shot-stopping, aerial control, and consistency.

Born in Tbilisi, Mamardashvili developed through the youth system at Dinamo Tbilisi, Georgia’s most decorated club. His performances at Locomotive Tbilisi where he was on loan caught the eye of Spanish scouts, and he joined Valencia in 2021. Although expected to start with the reserves, a string of impressive pre-season displays led to a surprise starting role on the opening day of the 2021/22 La Liga season. In his first La Liga campaign, Mamardashvili featured in 18 matches, keeping eight clean sheets and helping Valencia finish mid-table. Over the following three seasons, he cemented himself as first-choice goalkeeper, making 109 league appearances and ranking among La Liga’s best for save percentage. On 28 January 2024, Mamardashvili etched his name into the club’s history books by making his 60th consecutive La Liga start, becoming the Valencia goalkeeper with the most consecutive La Liga appearances in the club's history breaking José Manuel Ochotorena's previous record of 59 starts. He went on to play 69 league matches in a row.

Following his standout performances throughout the 2023/24 season, Mamardashvili was nominated for the Yashin Trophy — the annual award presented by France Football to the world’s best goalkeeper. At the Ballon d'Or ceremony held in Paris, he finished in seventh place. Valencia experienced another turbulent season in 2024/25, during which Mamardashvili remained at Valencia following his transfer to Liverpool on 27 August 2024, set to join the Reds on 1 July 2025. One of his most memorable performances came against Real Madrid at the Bernabéu, where he produced nine vital saves — including a penalty stop from Vinícius Jr. — to help Valencia earn a surprise result. It was one of several standout displays that underlined his growing maturity and composure on the big stage, further solidifying his reputation as one of Europe’s elite goalkeepers.