As a player he grew in the youth side of Partizan Belgrade. He played for BASK-u, Radnicki, Kolubari and Slavonka (Osijek) before flying to New Zealand in 1989 with his wife.
As a player, Vučinić was voted to the NBL All-Star Five in 1990. He has won five NBL Coach of the Year titles while guiding Nelson to two titles in 1998 and 2007. He stood down as Giants coach after their most recent success and still holds the record for most NBL coaching wins (164). After six years as an assistant coach, he took over the Tall Blacks reins in 2007, taking them to victory over Australia in the 2009 FIBA Oceania Championship and into the last 16 at the 2010 FIBA World Championship.