She was born in Zagreb and studied in the Academy of Drama Art there. She completed an MA in Writing for Performance at Goldsmiths College, University of London. She has taken part in theatre events such as Future Perfect, the Paines Plough Young Writers Programme and the Royal Court's 50th Anniversary season. Štivičić has written plays both in her native Croatian and in English.
Her major works in English include: Can't Escape Sundays, Perceval, Psssst, Two of Us, Goldoni Terminus, Fragile!, and Fireflies. Her plays have been produced in at least ten European countries. Fragile!, directed by Matjaž Pograjc and produced by Mladinsko Theatre, has won several awards at festivals in Croatia and Slovenia. In 2007, she co-wrote the play Pijana noć 1918 (Drunken Night 1918) with her father Ivo Štivičić for the Ulysses Theatre, Zagreb. Her project Goldoni Terminus was shown at the 2007 Venice Biennale.