Yvar-Emilian Mikhashoff was born Ronald MacKay in Troy near Albany, New York in 1941. He began piano studies with Betty Weir and Stanley Hummel in Albany. At the Eastman School of Music in 1959, he first took a major in composition and cello, then changed to piano studies with Armand Basile. In the 1961 academic year, he studied piano at the Juilliard School in New York City. He also had a career as a ballroom dancer from 1962-1965.

In 1964 Mikhashoff entered the University of Houston for studies in piano with Albert Hirsh. He earned a B.M. in 1967 and continued with graduate study in composition with Elmer Schoettle and obtained his M.M. in 1968. It was during this period that MacKay adopted his grandfather's name, Mikhashoff.

Receiving a Fulbright scholarship in 1968, he studied the music of the French Impressionists with Nadia Boulanger. After his return to the United States, Mikhashoff entered the University of Texas at Austin as a doctoral candidate in composition and studied with Hunter Johnson, Kent Kennan, Janet McGaughey and Karl Korte. He earned a Doctor of Musical Arts degree with a major in composition and a minor in literature in August 1973 and founded the Cambiata Soloists ensemble. In the fall of 1973 Mikhashoff was appointed Assistant Professor in the Music Department at the State University of New York at Buffalo. Based in Buffalo until his death in 1993, Mikhashoff had an international performing career which led him to promote new music and American music around the world.

Mikhashoff had a genius for programming, a talent he utilized extensively while organizing many festivals and broadcasts of new music throughout the world, including his work at the Almeida Festival in London and the Holland Festival. Mikhashoff co-founded the North American New Music Festival in 1983 with Jan Williams and remained a co-director until his death. He commissioned works from such notable composers as John Cage, Lukas Foss, Otto Luening, Poul Ruders, James Sellars, Christian Wolff, and many others. One of his most notable commissioning projects occurred in 1982 when he commissioned or solicited new tangos for solo piano from an international array of more than 80 composers. Mikhashoff also edited publications of music, including works by Henry Cowell, Lejaren Hiller, Conlon Nancarrow, and Virgil Thomson. He recorded on the New Albion, Mode, RCA Victor, CRI, and Spectrum record labels. Yvar Mikhashoff's support of contemporary music continues today through the Yvar Mikhashoff Trust for New Music which was created by his estate to support composers and performers of new music.