Kuzmić started his senior career in Borac Banja Luka and the first basketball steps began in Findo Doboj.

In 2011, he signed with Unicaja Málaga but played the 2011–12 season with farm team, Clínicas Rincón Benahavís of the Spanish Second League.

[5][6] To add to his D-League title, he was part of Golden State's championship winning team who defeated the Cleveland Cavaliers in the 2015 NBA Finals.

[15][16] On October 24, 2019, Kuzmić made a season debut against Barcelona, less than four months after sustaining severe injuries in traffic accident.

[20][21] In June 2014, national team head coach Aleksandar Đorđević included him on the preliminary 29-player list for the twelve 2014 World Cup roster spots.

[22] Three weeks later, in early July 2014, Kuzmić further made Đorđević's shortened list of 20 players invited for the training camp,[23] however, a fibula injury he picked up during the 2014 NBA Summer League ruled him out.

[25] In the first phase of the tournament, the team led by head coach Aleksandar Đorđević dominated its round-robin group with a 5–0 record, and then eliminated Finland and Czech Republic in the round-of-16 and quarterfinal games, respectively.

[31] In the morning hours of 14 July 2019 on the Banja Luka-Prijedor state road near the village of Ramići, Kuzmić was involved in a serious traffic accident.

Driving his Porsche SUV, the twenty-nine-year-old professional basketball player reportedly collided with a BMW vehicle going in the opposite direction while traveling at a high speed.

[32] He sustained life-threatening injuries in the accident, breaking his maxilla and mandible head bones (upper and lower jaws), as well as his chest.