Kupšas played for Lietkabelis in the 2012–13 season and averaged 10.5 points, 5.5 rebounds and 0.8 blocks per 21 minutes of game action.

On February 7, 2017, he parted ways with Vytautas to join CB Clavijo of the Spanish LEB Oro.

On August 14, 2019, Kupšas signed a one-year deal with Hapoel Jerusalem of the Israeli Premier League.

[7] On March 2, 2020, Kupšas parted ways with Hapoel Jerusalem to join Filou Oostende of the Belgian Pro Basketball League.

[15] On June 27, 2024, Kupšas signed one–year contract with Šiauliai of the Lithuanian Basketball League (LKL).