Born in Banja Luka, SR Bosnia and Herzegovina. In 1997, Saša began his football career playing for Rudar Prijedor as a 16-year-old. He made his debut against FK Glasinac Sokolac. Stević played for Rudar Prijedor until 2001 when he moved to Serbian club FK Borac Čačak where he played from 2001 until 2005. Then, he moved to Finland to play in Veikkausliiga club FF Jaro where he played the seasons 2005 and 2006. In 2007, he moved to another Finish club IFK Mariehamn.
In summer 2008 he returned to the Serbian SuperLiga by joining FK Banat Zrenjanin. Played there season and half. And on winter transfers window 2010 he moved to Romania by joining Liga I side Ceahlăul Piatra Neamţ where he played the rest of the season. In summer 2010 he moved to Ukraine and joined FC Volyn Lutsk.
He played much of his career in a central midfield role, but he has also been used as a central defender.
