Chevrevski was born on 17 May 1951 in Skopje. He graduated from the Faculty of Dramatic Arts in Skopje and received his film training at the University of California, Los Angeles (UCLA). He also worked as a professor at the Faculty of Dramatic Arts in Skopje and was dean of the Faculty.

He starred in several Yugoslav and Macedonian films, including The Assassination at Sarajevo (1975), The Longest Journey (1976), The Verdict (1977), The Partisan Squadron (1979), The Lead Brigade (1980), The Red Horse (1981), Hi-Fi (1987), Tattoo (1991), Gypsy Magic (1997), Mirage (2004), Punks Not Dead (2011), Children of the Sun (2014), Second Chance / Vtora Sansa (2019), the TV series Trieste via Skopje (1987), Dogs Bark, but the Caravans Move On / Psi laju, vetar nosi (2017) and many more. His last film role was in Veljko Bulajic`s Escape to the Sea.  

Chevrevski was one of the founders of the private film production company Triangl and also produced the films of Stole Popov - Gypsy Magic and To the Hilt / Do balcak.

He won several awards for his work. In 2019 he received the Prize for Outstanding Achievement in Film from the International Film Festival Asterfest in Strumica.