In his club career, he won numerous titles in European club competitions. In addition to having played together for their Yugoslav national team, Mirza Delibašić and Dražen Dalipagić, also played together with Real Madrid. Their performance in a 1981 Euroleague game versus Cibona, in Zagreb, is only one of the many highlights of their careers.
In that game, Delibašić scored 26 points and Dalipagić 33. The game appropriately finished with a two-on-one fast-break, with Delibašić making a behind-the-back fake pass to Dalipagić, and passing by a defender for a two-handed dunk at the buzzer. Cibona's fans put aside their team's loss in the game, and showed their appreciation for the Bosnian stars performances, with a standing ovation at the end of the game.
In August 1983, Delibašić suffered a near-fatal brain hemorrhage, and he had to permanently retire from the sport he loved. He lived in Sarajevo throughout the 1992-1996 siege of the city. His final years were marked by persistent health problems, due to his heavy drinking, which led to his death in 2001, at the age of 47, in Sarajevo. Several thousand people attended his funeral in Sarajevo, and Bosna renamed its arena, in his honor.