Savić made first career steps as a basketball player with Čelik in the First League of Yugoslavia.

In 1991, he left Yugoslavia and Pop 84, and signed with FC Barcelona, where he spent a couple of seasons with them playing in Spain's Liga ACB.

In 1993, he reached with FC Barcelona, the semifinals of the FIBA Korać Cup, where they were eliminated by Virtus Roma and Dino Rađa.

He then spent a year with the Spanish club Real Madrid, before settling in Italy, with Kinder Bologna, in 1996.

[1] Savić then returned to FC Barcelona in 2000, and then moved to the Italian club Skipper Bologna in 2001.