After learning piano for some time, he decided to study clarinet with Philipp Dreisbach at the Stuttgart Hochschule für Musik (1928/1929).

In an interview, Raschèr said, "Obeying necessity, not following my inclination, I started to play saxophone in order to be in a dance band.

In April 1936 he participated in the XIV Festival of the International Society for Contemporary Music (ISCM), premiering the work Concertino da camera by Jacques Ibert.

[3] Raschèr arrived in the United States in 1939 and made his American debut on 20 October 1939 with the Boston Symphony Orchestra conducted by Serge Koussevitzky.

On 11 November 1939 he was a featured soloist at Carnegie Hall with the New York Philharmonic under the baton of Sir John Barbirolli.

[3] His career continued with solo appearances in Washington, D.C. and at New York City's Town Hall in the spring of 1940, which Arturo Toscanini attended and thereupon embraced Raschèr.

His international career as a soloist and his ability to gain residence and citizenship in many countries could have been damaged or destroyed if any suspicion arose about his background.

As Raschèr's reputation grew in the United States, he also performed many orchestra concerts as soloist as well as with various university bands.

Raschèr performed as soloist with more than 250 orchestras and wind ensembles worldwide, including concerts in Europe, Asia, Australia, Canada and the United States.

Throughout the middle decades of the twentieth century, a preponderance of the significant new saxophone solo and chamber repertoire would appear with the familiar dedication to Sigurd M. Raschèr, the outcome of not just his ongoing commitment to motivate some of the world's finest composers, but also in part the result of genuine close friendships he developed with so many.

His students and other disciples felt that the desirable tone for a classical saxophone was a softer, rounder sound—a sound that can only be produced by a mouthpiece with a large, rounded interior (often referred to as an "excavated chamber").

There were other ways in which his playing differed from the majority of classical saxophonists; these included his insistence on using the slap tongue as a pizzicato technique, and his use of flutter-tonguing.

For a period of time the only large-chambered mouthpieces were ones that had been manufactured in the 1920s and 1930s, leading Raschèr students to search pawn shops and other sources of old instruments.

This upper range became known as the "altissimo register," but Raschèr himself refused to use that term, preferring to call them "top tones."

Despite the initial resistance on the part of the saxophone community to the altissimo register, it has since come to be an accepted technique, and is utilized by nearly all classical and jazz saxophonists.

During the earlier decades of his career, many saxophonists resisted and even ridiculed his pioneering work in extending the upward range of the instrument beyond two and a half octaves.