Savvidis was born on February 8, 1961 in Lefkosia, Cyprus. He played as a midfielder, starting his career with Olympiakos Nicosia. He made his debut for Omonia Lefkosia in 1981. His fine play earned him a transfer to AEK Athens, in the Greek Alpha Ethniki, after the 1987 season. At the time, he was considered the best footballer in Cyprus.
During his career, Savvidis was capped 46 times by the Cyprus National Football Team, scoring two goals.
He left Digenis to pursue a career as assistant manager to former AEK teammate Toni Savevski: 2001-02 with Apollon Limassol and between 2002-2004 with Omonia. In late November, 2007, he was named head coach of Omonia, a position he held until March 2008.