He debuted at the 2016 European Championship in Poland as the second choice goalkeeper to Mirko Alilović, but he ended up being the biggest reason for his country winning the bronze medal.

Stevanović grew up in the neighborhood of Trsat across the street from Dvorana Mladosti then the venue of RK Zamet.

In 2007 Stevanović moved to Poreč where he maintained a vital role in the clubs great results and qualification for the Challenger Cup.

[6] He also spent a season in Slovenian club RD Krško where he was trained by head coach Željko Babić.

On 5 December 2016 it was confirmed that Stevanović had signed a three-year contract with Swiss club Kadetten Schaffhausen stating that he would be leaving RK Zagreb at the end of the season.

[11] He competed at the 2016 European Men's Handball Championship as a replacement for Filip Ivić who was injured.

[13] In August of the same year he played for the national team at the 2016 Summer Olympics in Rio de Janeiro where Croatia finished in fifth place.

[18] On 26 January 2019 he confirmed he is going to retirement of the Croatian national team after 2019 World Men's Handball Championship.