Wurf was born in New York City in 1919. The son of immigrants from the Austro-Hungarian Empire, he developed polio at the age of four.
Wurf began a career in the American labor movement as a hotel worker organizer in New York City. He went to work for AFSCME in 1947, then rose through the ranks of New York City's District Council 37 to become its president. In 1958, Wurf wrung from mayor Robert F. Wagner, Jr. an executive order giving the city's workers the right to form unions, and providing for elections which could establish these unions as exclusive bargaining agents for the workers in various city agencies. District Council 37 won many of the ensuing elections, making it into one of the large public employee local unions in the world.
Wurf was extremely active in the American civil rights movement. He helped establish the first New York state chapter of the Congress of Racial Equality (CORE) in the late 1940s. He was a close associate of Martin Luther King, Jr., and King was attending an AFSCME sanitation strike when he was assassinated in 1968. "Let us never forget that Martin Luther King, on a mission for us, was killed in this city. He helped bring us this victory," Wurf later said.
Wurf became president of AFSCME in 1964 as the head of a group of "Young Turks" committed to changing the organization into an effective union. Through energetic organizing and aggressive bargaining, AFSCME grew rapidly under his leadership from about 220,000 members to just over one million in 1981.
Gerald W. McEntee succeeded him as president of AFSCME.