Savcic swam only in the 100 m breaststroke, as a member of the former Yugoslav squad, at the 2000 Summer Olympics in Sydney. He achieved a FINA B-standard entry time of 1:04.75 from the Akropolis International Meet in Athens. He challenged seven other swimmers in heat four, including two-time Olympians Valērijs Kalmikovs of Latvia and Arsenio López of Puerto Rico. He raced to the fourth seed by a 0.62-second deficit behind joint winners Kalmikovs and Lopez in 1:04.64, worthy enough for a Yugoslav record. Savcic failed to advance into the semifinals, as he placed forty-second overall on the first day of prelims.