Beckwith studied at the Royal Conservatory of Music, and obtained a Masters in Music from the University of Toronto. He went on to work as a lecturer, professor, Dean and the first Director of the Institute for Canadian Music with the Faculty of Music at the University of Toronto between 1952 and his retirement in 1990. Beckwith has created over 130 compositions, which range in genre from stage and orchestral to chamber, solo, and choral music. He was involved with Music at Sharon, a summer concert series near Newmarket Ontario, where he composed and performed over 200 arrangements of folk music of Canadian heritage between 1981 and 1991. Additionally, Beckwith has collaborated with notable Canadian writers such as James Reaney, Jay Macpherson, Margaret Atwood, and Dennis Lee.