Suter's compositions contain echoes of Brahms, Strauss, Mahler, and many other composers who Suter conducted at Basel. Much of his output is for chorus, both accompanied and unaccompanied; the best-known of his works is the oratorioLe Laudi (The Praises) or Le Laudi di San Francesco d'Assisi, based on the Canticle of the Sun, written in the summer of 1923 in Plaun da Lej, in Engadine, and premiered on 13 June 1924 in Basel. By 1930 the oratorio had been performed over eighty times in nearly as many cities. Wilhelm Furtwängler led the Vienna premiere, and the work was acclaimed in Paris, Stockholm, Berlin, Hamburg, Leipzig, Cologne, and a host of smaller German cities. Other compositions include a symphony (1914), a violin concerto (1921), three string quartets (1901, 1910, 1921), a sextet for strings (1920), and numerous songs.
The first US performance of Le Laudi may have been in 1930 at St. Mark's Church, New York City; no details of that performance are available.
The first professional performance of Le Laudi in the US was in June, 2000, at Neil Blaisdell Concert Hall, Honolulu, Hawaii, with singers of the Honolulu International Choral Festival, soloists Zofia Kilanowicz, soprano, Milagro Vargas, mezzo-soprano, Stuart Neil, tenor, and Leslie 'Buz' Tennent, baritone, the Honolulu Boy Choir, and members of the Honolulu Symphony, Timothy Carney, conducting.
The American Symphony Orchestra gave the US Premiere of Suter's Violin Concerto, Op. 23 in 2008. 
The UK premiere of Le Laudi took place in Cambridge on 21 June 2009, by Choir 2000 under the direction of Peter Britton.