Early on as a young child, Mischa Damev was given his first music lesson by his grandfather, the well-known Bulgarian director Michael Lefterov. At the age of 10, Mischa Damev moved with his family from Sofia to Switzerland. He completed his piano studies at the Basel Academy of Music with a soloist diploma, afterwards studying with Alexis Weissenberg in Paris and Nikita Magaloff in Geneva.

From 1990 to 1999, Mischa Damev occupied the role of artistic director of the International Orpheum Music Festival for the Advancement of Young Soloists in Zurich. From 1992 to 2007, he led the Lilienberg recital series and the Lilienberg Foundation Art and Culture Division in Ermatingen.

Following the advice of his mentor Mariss Jansons, he turned his attention to conducting in 1991, when he began studying with Karl Österreicher in Vienna. Following his successful debut with the Bulgarian National Radio Orchestra and the Sofia Opera House, Mischa Damev spent several years working as an assistant to Mariss Jansons, Georges Prêtre and Vladimir Fedosejev.

During the 2004-2005 season, Georges Prêtre and Mischa Damev jointly led the production of "Carmen" at Santa Cecilia in Rome and "Pelléas and Mélisande" at La Scala in Milan. From 2006 to 2009, Mischa Damev and Jon Lord (Deep Purple) worked together closely on many European stages.

In 2006, Mischa Damev occupied the role of CEO of the Unternehmerforum Lilienberg (entrepreneurial forum) in Ermatingen. Since 2007, Mischa Damev has worked as director of the Migros Culture Percentage Classics of the Federation of Migros Cooperatives; in 2019, he also assumed the position of director and artistic director of the Septembre Musical festival in Montreux-Vevey.