In 1981 he joined the Zagreb powerhouse Cibona where Mirko Novosel was starting to build the future European champion team with players like the veteran Krešimir Ćosić, Aleksandar Petrović, Dražen Petrović, Andro Knego, Mihovil Nakić and Branko Vukićević.

For their second European trophy Cibona defeated Real Madrid in the final again with Čutura scoring 16 points.

Čutura won his second European champion title in 1986 participating with 16 points in the final victory against Žalgiris.

Čutura's second major tournament was the first World Under-19 Championship, held the same year in Brazil where Yugoslavia finished fourth.

He was once again the top scorer (22.8 p) of his team (even though still playing for a second division club) at the 1980 European Championship for Juniors where he won silver.

[3] At the 1989 Eurobasket played in front of his hometown crowd Čutura (5.0 ppg) along with Dražen Petrović, Dino Rađa, Žarko Paspalj, Vlade Divac, Predrag Danilović, Toni Kukoč, Jure Zdovc and others took gold.

After the breakup of Yugoslavia, Čutura never made a major tournament squad for the Croatia national basketball team.