Savić started his senior career with Dinamo Pančevo, before moving to Proleter Zrenjanin in 1994.
The duo would move to Israeli club Beitar Jerusalem in the summer of 2000, before returning to Partizan the next season.
During his second spell with the Crno-beli, Savić helped the team qualify for the 2003–04 UEFA Champions League.
[1] In 2004, Savić moved abroad for the second time by joining Chinese club Liaoning Zhongyu.
Savić started his managerial career at Serbian League Vojvodina club Vršac in early 2015.