At 19 he began his professional playing career with the Hess String Quartet, and toured as a violin soloist in Switzerland, the Netherlands, and Germany.

Stoessel enlisted in the United States Army in 1917, becoming a lieutenant in the 301st Infantry American Expeditionary Forces and leader of the regimental band at Camp Devens.

He became director of the AEF Bandmaster's School of Chaumont, France, organized by Walter Damrosch, after studying there with André Caplet.

He conducted the United States premiere of the Piano Concerto in D flat by Aram Khachaturian, on 14 March 1942, with soloist Maro Ajemian and the Juilliard Graduate School.

[2] It was while on stage conducting an orchestra for American Academy of Arts and Letters in New York, that Stoessel died of a heart attack on May 12, 1943.