Schumann's intention was to pursue a career as a virtuoso pianist, having been assured by his teacher, Friedrich Wieck, that he could become the finest pianist in Europe after only a few years of study with him. However, when a hand injury prevented those hopes from being realized, he decided to focus his musical energies on composition.

Schumann's published compositions were written exclusively for the piano until 1840; he later composed works for piano and orchestra; many lieder (songs for voice and piano); four symphonies; an opera; and other orchestral, choral, and chamber works. His writings about music appeared mostly in the Neue Zeitschrift für Musik ("New Journal for Music"), a Leipzig- based publication that he jointly founded.

In 1840, after a long and acrimonious legal battle with his piano instructor (Wieck), Schumann married Wieck's daughter, pianist Clara Wieck, who also composed music and had a considerable concert career.

For the last two years of his life, after an attempted suicide, Robert Schumann was confined to a mental institution at his own request.

In 1974, Sauer was named Principal Trombonist of the Los Angeles Philharmonic by Zubin Mehta. He made his Los Angeles Philharmonic concerto debut in 1979, performing Kazimierz Serocki's Concerto for Trombone and Orchestra with Zubin Mehta conducting - a work whose U.S. premiere Sauer gave at the Eastman School of Music in 1965. In March 2003, Sauer premiered Augusta Read Thomas’s Trombone Concerto with the Los Angeles Philharmonic, conducted by Esa-Pekka Salonen. He was also a frequent performer with the Philharmonic's New Music Group. He retired from the orchestra in 2006.

Sauer has appeared as soloist with many orchestras and has given master classes and recitals throughout Europe, Scandinavia, Japan, Mexico, Costa Rica, Canada, and the United States. He has appeared at the Stratford, Marlboro, and Aspen summer music festivals and was visiting professor at the Eastman School of Music as well as an instructor with the New World Symphony (Miami) and the International Brass Festival in Melbourne (Australia). Currently, Sauer is on the faculty of Music Academy of the West and Arizona State University. He has taught many prominent trombonists, including Christian Lindberg.

Sauer is a founding member of Summit Brass, and is a clinician for Shires trombones.

He is featured on a number of recordings, including:
A recording of works by Teleman, Handel, Haydn, and others (with Zita Carno on keyboards) (Crystal Records)
The Mahler Symphony No. 3 , with Esa-Pekka Salonen conducting the Los Angeles Philharmonic (with Anna Larsson, contralto; Donald Green, posthorn; Martin Chalifour, violin; Paulist Boy Choristers of California, Women of the Los Angeles Master Chorale) (Sony Classical)

Two discs of orchestral excerpts for trombone with commentary (Summit Records, OrchestraPro series). These are among the most sought after discs for those preparing for orchestral trombone auditions.