Tamari Tatuashvili played for the clubs FC Norchi Dinamo Tbilisi, FC Iveria Khashuri and FC Dinamo Tbilisi. She enjoyed in the 2007–08 season the Georgian champion title with FC Dinamo Tbilisi. Later, she transferred to FC Baia Zugdidi, which became champion in the 2009–10 season. Following the dissolution of the Georgian women's league in 2010, she moved to Turkey, and signed with Lüleburgaz 39 Sporr to play in the 2011–12 Turkish Women's First Football League. The next season, she was transferred by Adana İdmanyurduspor. After appearing two full seasons and a half season for the Adana-based team, she moved in February 2015 to İlkadım Belediyesi in Samsun.[1]
After her team was relegated to the Second League at the end of the 2017–18 season, she transferred to the newly promoted First League club Hakkarigücü Spor in October 2018.[1][3]
Tamari Tatuashvili was called up to the Georgia women's under 17 team, and played her first match against the girls from England at the 2008 UEFA Women's Under-17 Championship – Group round on October 27, 2007.[2] She capped three times in the tournament.