Jevtić was born in the settlement of Kovačevac in Mladenovac, SFR Yugoslavia. He began acting in 1998, and was since active in the Atelje 212 theatre in Belgrade. In 2001, he graduated from the Belgrade Academy of Dramatic Arts. A student of Biljana Mašić, his first role was Euclio in Aulularia. He later landed lead roles in various theatre productions, for which he earned numerous awards. For his performance in Okamenjeni princ in the Duško Radović theatre, he received the Miloš Žutić Award. As Prince Hamlet in Hamlet, he won the Ardalion and the Serbian Oscar of Popularity in 2011. He was awarded the Serbian Oscar of Popularity again for his Romeo Montague interpretation at the Novi SadSerbian National Theatre. The Noises Off rendition gained him a Zoran Radmilović Award and Ljubinka Bobić Award in 2014. He has taken part in over sixty international film and theatre festivals, and has completed over one hundred performances in the Atelje 212 theatre. He has performed in Moscow, London, Verona, Rome, Split, Budapest, Dresden, Vienna and Zagreb. In 2018, he starred as Friedrich Nietzsche in his directorial debutKad je Niče zaplakao at Atelje 212. He further rose to continental prominence as homosexual activist Mirko Dedijer, in the 2011 Festroia Award-winning film The Parade. The film by Srđan Dragojević reached commercial success, despite the controversial subject, and critics praised Jevtić's portrayal. Other than his role in The Parade, he actively appeared in the We're Not Angels films as fictional Leskovac native Andreja and played the supporting role of Mitar in the 2011 American war film In the Land of Blood and Honey directed by Angelina Jolie. He won the Apolon Prize in Belgrade for his role as Miloš in Life Is a Miracle entered into the 2004 Cannes Film Festival. He starred as Dane in the Srđan Dragojević production Sveti Georgije ubija aždahu in 2008, and in Na lijepom plavom Dunavu in 2009 as Jacek. His repertoire on television includes Sisyphus in The Myth of Sisyphus from 2009 to 2011, cameo roles in Porodično blago, the secondary character Nebojša in Samo Era from 2008 to 2012, and Djoni in The Mask. Jevtić is one of the most prominent voice actors in Serbia, with notable roles voicing the Serbian dub of Sebastian in The Little Mermaid franchise, Banzai in The Lion King franchise, Genie in the Aladdin franchise, Kuzco in the Emperor's New Groove films, Randall Boggs in the Monsters Inc. films, King Candy in Wreck It Ralph, Elliot in Open Season, Marty in the Madagascar films, King Louie in The Jungle Book, Master Crane in the Kung Fu Panda franchise and Barry Benson in Bee Movie. He has also voiced Ash Ketchum in the Serbian dub of Pokémon. Until being convicted of sex offences in 2020, he was a docent at the Academy of Dramatic Arts in the University of Belgrade, and worked there as a professor of acting and diction.
