Born in Omiš, Mimica had enrolled at the University of Zagreb School of Medicine before the outbreak of World War II. In 1942 he joined Young Communist League of Yugoslavia (SKOJ) and in 1943 he went on to join the Yugoslav Partisans, becoming a member of their medical units.

After the war Mimica wrote literary and film reviews, and his career in filmmaking began in 1950 when he became the director of the Jadran Film production studio.

He had his directorial and screenwriting debut in the 1952 Yugoslav film In the Storm (Croatian: U oluji) which starred Veljko Bulajić, Mia Oremović and Antun Nalis. In the 1950s Mimica worked as a director and writer on a number of critically acclaimed animated films and became a prominent member of the Zagreb School of Animated Films (his 1958 animated short film The Loner (Samac) was awarded the Venice Grand Prix), along with authors such as Vlado Kristl and Academy Award-winning Dušan Vukotić.

Mimica made several other films through the 1970s, most notably the period films Anno Domini 1573 (Peasant revolt of 1573) – Seljačka buna 1573. in Croatian – depicting the 16th century Croatian-Slovenian peasant revolt, and The Falcon (Banović Strahinja), set in 14th century Serbia, before retiring from filmmaking in 1981.