He studied Turkic languages at the Oriental Institute in Vienna, receiving his doctorate in linguistics and social anthropology in 1944 for a dissertation on Uzbek.

After reading some works by Sidney Herbert Ray, Wurm became interested in Papuan languages and began a correspondence with Arthur Capell, a lecturer in linguistics at the University of Sydney.

Wurm began teaching himself Tok Pisin and Hiri Motu from books and took up a position in London.

In 1957, the Wurms moved to Canberra, where Stephen took up a post as Senior Fellow within the Research School of Pacific and Asian Studies (RSPAS, now Coral Bell School of Asia Pacific Affairs) at the new Australian National University (ANU).

[3] He was appointed a member of the Order of Australia in the 1987 Queen's Birthday Honours, for "service to education, particularly in the field of linguistics".