During his playing days, Slišković was considered one of the most technically gifted players of his generation. In 1985, he was named the Yugoslav Footballer of the Year. He had the most success while playing for hometown club Velež Mostat and Croatian club Hajduk Split. With Velež, Slišković won the 1980–81 Yugoslav Cup and the 1980–81 Balkans Cup, while with Hajduk he won the 1983–84 Yugoslav Cup and was also part of the Hajduk team that made it all the way to the semi-finals of the 1983–84 UEFA Cup.