Born into a middle-class family, Tchaikovsky was educated for a career as a civil servant, despite his obvious musical precocity. He pursued a musical career against the wishes of his family, entering the Saint Petersburg Conservatory in 1862 and graduating in 1865. This formal, Western-oriented training set him apart from the contemporary nationalistic movement embodied by the influential group of young Russian composers known as The Five, with whom Tchaikovsky's professional relationship was mixed.

Although he enjoyed many popular successes, Tchaikovsky was never emotionally secure, and his life was punctuated by personal crises and periods of depression. Contributory factors were his suppressed homosexuality and fear of exposure, his disastrous marriage, and the sudden collapse of the one enduring relationship of his adult life, his 13-year association with the wealthy widow Nadezhda von Meck. Amid private turmoil Tchaikovsky's public reputation grew; he was honored by the Tsar, awarded a lifetime pension and lauded in the concert halls of the world. His sudden death at the age of 53 is generally ascribed to cholera, but some attribute it to suicide.

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.