Savić graduated saxophone at the Academy of Arts in Novi Sad, and clarinet at the Faculty of Music in Belgrade. During his musical development, he attended many schools and seminars abroad with renowned professors.

Since 2006 he has been working as a professor of clarinet and saxophone at the Music School Josip Slavenski, and his students have won many awards at republic and international competitions.

Savić held masterclasses in Serbia and abroad: Alpen Classica Fest – Italy, Olympic Sax Festival – Greece, University of Hartford – USA. He performed as a soloist at music festivals throughout Serbia, and held concert series in France, Italy, and the US.

He performed as a soloist with the Belgrade Philharmonic, RTS Symphonic Orchestra, chamber orchestra Metamorphosis, recorded music for Radio Belgrade, and presented premieres of works by Ivan Jevtić, Ivan Brkljačić, Aleksandar Sedlar, and others. As an orchestra musician he has engagements in the Belgrade Philharmonic and RTS Symphony Orchestra, performing at concerts and tours in Serbia and abroad.

Milan Savić is the founder and director of the international saxophone festival – Belgrade Saxperience. The festival aims to educate young saxophonists, enrich the saxophone repertoire, promote the various possibilities of saxophone and hosts the most important saxophonists of today. In 2017, Milan Savić was awarded by the French Ministry of Culture and Literature as Knight of Arts.