Savevski is widely regarded as one of the best foreign midfielders to have played in the Greek soccer league. He signed for AEK Athens in 1988 and was a regular for 13 years playing in 358 league games and winning four times the Greek championship (1989, 1992, 1993, 1994) and three times the Greek cup (1996, 1997, 2000).
After he retired as a player, Savevski became a manager in the Greek and Cypriot leagues. In the 2002 season he was the coach for Apollon Limassol FC and between 2002-2004 coach of Omonia Nicosia. In 2003 he won the Cypriot championship and Cyprus Super Cup with Omonia. He currently works for AEK coaching in its youth academy system.