Born in Tuzla to Bosnian Muslim parents, father Izet Delibašić from Kakanj and mother Zajkana "Duda" Mehičević from Ljubuški, young Mirza took up tennis and excelled at it. By the age of fourteen, he switched to basketball.
Club career
Mirza Delibašić, nicknamed Kinđe, led his club Bosna to the EuroLeague Championship in 1979. He played his first games at age of 15 for KK Sloboda Dita, Tuzla's basketball club. Three years later, in 1971, he signed a contract with KK Bosna. After leaving Bosna, Delibašić went to the Spanish Primera División, where he ended up being considered one of the best players ever to play for Real Madrid, along with the likes of Juan Corbalán, Wayne Brabender, Fernando Martín Espina, Fernando Romay, Dražen Petrović, and Arvydas Sabonis. 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 1983 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.
Career ending
In early summer 1983, the then twenty-nine-year-old Delibašić left Real Madrid and signed with the Italian League club JuveCaserta, which was at the time coached by his former Bosna mentor Bogdan Tanjević. In August 1983, the team went to preseason training and conditioning, to the town of Bormio, in the Italian Alps. After coming back south to Caserta, following the grueling altitude training, Delibašić suffered a near-fatal brain hemorrhage that would turn out to be career-ending. Being in a critical condition, a private plane was immediately organized for him to be airlifted to the Military Medical Academy in Belgrade, where he was hospitalized for months. He survived and recovered, but not enough to return to playing basketball, thus forcing him to permanently retire from playing, effective immediately.
In the late 1970s, Delibašić married his girlfriend Branka. Their son Dario was born in December 1979. The couple divorced in 1980, after Delibašić moved abroad to play with Real Madrid. In 1986, Delibašić, then retired from playing basketball and performing an administrative role at KK Bosna, married Slavica Šuka, an active basketball player with ŽKK Bosna. The same year in October, the couple had a son named Danko. Delibašić's 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. He is interred next to singer Davorin Popović, in the Alley of Greats at Bare Cemetery. His funeral was attended by thousands. After his death, KK Bosna renamed its arena in his honor.