His compositions include Hiawatha, a symphony for orchestra and vocal soloists, as well as incidental music for plays, piano works, songs, and several operas.

Born in Berlin, Stoepel worked in Paris and London, but spent a large portion of his career in New York City where he died at the age of 66.

In 1856 the New York Times reported: "The orchestra of this establishment [i.e., Wallack's Theatre] is deliciously neat and effective, and the compositions it plays are thoroughly artistic.

Mr. Robert Stoepel, the conductor, is one of the best informed musicians in the country, and the evidence of taste and knowledge are never absent.

He has succeeded in making the musical department an important feature of the entertainments, and if the orchestra always plays as well as it did on Saturday night we are not at all surprised thereat.

"[6] He wrote incidental music for all of the plays written by Dion Boucicault during his stay in New York from 1854 through 1860.

[7][8] Subtitled "an Indian Symphony," this was a work symphonic in proportions with vocal soloists and a part for narrator.

Harwood (who alternated between the two female roles of Nokomis and Minnehaha), Harrison Millard (Hiawatha), J. Q. Wetherbee (who sang the Great Spirit and the Arrow-Maker)[3] with recitations by the composer's wife Matilda Heron, on 21 February 1859 at the Boston Theatre in Boston.

There he composed and conducted incidental music for the stage productions The Hurricane, Divorce, Frou-Frou, Man and Wife, and Fernande.