Mansurian was born in Beirut, Greater Lebanon on January 27, 1939. His family moved to the Armenian SSR in 1947 and settled in Yerevan in 1956, where he continued his education. He studied first at the Romanos Melikian Music School under the Armenian composer Edvard Baghdasaryan and later at the Yerevan Komitas State Conservatory. During his years of study, he wrote different works of varied genres and was awarded for some of them.

He taught modern music theory at the Conservatory from 1967 to 1986. He was the Rector of the Conservatory from 1992 to 1995.

An ECM album of Mansurian's music, Monodia, was nominated for the 2004 Grammy Award for "Best Instrumental Soloist(s) Performance (with Orchestra)" and "Best Classical Contemporary Composition". In 2017, ECM's recording of Mansurian's Requiem was nominated for two Grammys. The Requiem received the Presidential Award of Armenia for its commemoration of the victims of the Armenian Genocide.

On January 27, 2024, a concert of the Armenian State Symphony Orchestra commemorating Mansurian's 85th birthday occurred at Aram Khachaturian Concert Hall in Yerevan. Included was his viola concerto, "...and then I was in time again", played by Sergey Poltavsky. The program concluded with excerpts of Mansurian's film music.