Beaser was brought up in a non-musical family. His father was a physician and mother was a chemist. He grew up in Newton, Massachusetts, where he distinguished himself at a young age as a percussionist, composer and conductor. He made his debut with the Greater Boston Youth Symphony at Jordan Hall when he was 16, conducting the premiere of his orchestral work Antigone. He went on to study with Yehudi Wyner and Jacob Druckman at Yale College, graduating summa cum laude, Phi Beta Kappa in 1976, and later received his Master of Music, M.M.A. and Doctor of Musical Arts degrees from the Yale School of Music. He studied conducting with Otto-Werner Mueller and William Steinberg. Other teachers included Toru Takemitsu, Arnold Franchetti, Goffredo Petrassi and Earle Brown. He studied with Betsy Jolas on a fellowship at Tanglewood. In 1977, Beaser became the youngest composer to win the Rome Prize from the American Academy in Rome. Residence in Rome proved a watershed in his development, and he embraced more tonal language, synthesizing a variety of diverse influences from jazz to folk into his work.