Augustincic was born in the small town of Klanjec . In 1918 he enrolled at the Arts and Crafts College in Zagreb, where he studied sculpting under professors Rudolf Valdec and Robert Frangeš. After the college became the Royal Academy of Arts and Crafts in 1922, he studied under the guidance of Ivan Meštrovic until his graduation in 1924. He then received a scholarship from the French government and continued his studies at the École des Arts Décoratifs and École des Beaux-Arts in Paris under the guidance of Jean Antoine Injalbert.

In 1925 and 1926 Augustinčic held his first exhibitions in Paris, before returning to Zagreb and exhibiting in Zagreb in 1926 and then again in 1927 in Lwów and Zagreb. In 1929 he was one of the founding members of the Earth Group  arts collective which brought together prominent left-oriented sculptors, painters and architects. Augustinčic took part in several exhibitions organised by the group between 1929 and 1933, when he left the group, two years before it was banned by the authorities in 1935.

In 1930  he creates intensively  public monuments,  the opus he started in 1928.

Participating and winning competitions, he gained a reputation as a master of the monuments (especially  equestrian statues which became one the hallmarks of his career) and earned him the status of state sculptor.

In 1940 he became a corresponding member of the Yugoslav Academy of Sciences and Arts (JAZU). In 1946 Augustinčic became a professor at the Academy of Fine Arts in Zagreb, and after the war he was made a member of the People's Assembly.

In 1970 Augustinčic donated his works to his native town of Klanjec, where a gallery exhibiting his works opened in 1976.

He died in May 11, 1979.