After dropping out of Detroit City College in 1933, Woodcock worked as a machine assembler. In 1941, he married his first wife Loula Martin with whom he had a son John and two daughters, Janet and Leslie. Divorcing Loula, Woodcock remarried in 1978, the a nurse Sharon Tuohy, to whom he remained married until his death.
In 1970, working his way up the ranks, Woodcock became first the International Vice President of the UAW from 1955-1970. Following this, from 1970-1977, he succeeded Walter Reuther as the fifth President of the UAW.
In 1977 Woodcock retired from the union and was named head of the United States Liaison Office in Beijing (which served as the de facto U.S. embassy in the People's Republic of China in the absence of full diplomatic relations) by U.S. President Jimmy Carter. After playing a pivotal role in negotiating the establishment of full diplomatic relations with the People's Republic of China in 1979. Woodcock, who served from 1979 to 1981, was the first United States ambassador to the communist Chinese state and the first ambassador to mainland China since 1949, when Leighton Stuart had been ambassador to the Republic of China.
Woodcock later taught at the University of Michigan. He lived in Ann Arbor with his wife Sharon until his death on January 16, 2001. Woodcock had three children, John Woodcock (ret. Maj Colonel, USAF), Janet Woodcock (Photographer) and Leslie Woodcock Tentler (Professor of History); a daughter- and son-in-law (Carol Collins, Framer, partner of Janet and Thomas Tentler, Professor of History, married to Leslie); three grandchildren (Sarah Tentler, Speechwriter; Gregory Tentler, Art Historian; and Daniel Tentler, Lawyer); and a godson, Daniel Miller (high school student).
Woodcock's name appeared on Nixon's enemies list at #9, with the annotation "No comments necessary".