He made first steps for KK Čelik in the First League of Yugoslavia. In 1990 and 1991 he played with Jugoplastika in Split, winning both the Yugoslav league title and the FIBA European Champions Cup (now known as the Euroleague) in each of the two years. In 1991, he signed with FC Barcelona and spent a couple of seasons in Spain.
After retiring from playing at Fortitudo in 2002, Savić became part of the club's management. He spent three years as the team's general manager. Savić is also one of the founding members of the Group Seven Children's Foundation. From 2005 until 2008 he was the general manager of FC Barcelona Bàsquet. From 2008 to 2009, he managed Fortitudo. He then became a sports agent, founding Invictus Sports Group.