Joseph Woosnam was born in Bootle, Lancashire, England on 17 August 1889. He was the son of Welsh parents, William Woosnam, a mariner, and the former Elizabeth Price. He had three elder brothers.
The 1901 census shows the Woosnam family living at 28 Holly Street in Bootle.
Woosnam went to sea as a young man and between 1906 and 1907 he worked as a waiter aboard both Saxonia and Carmania. In April 1912 he was serving as a waiter aboard the eastward-bound voyage of the Carpathia when that ship rescued the survivors of the Titanic.
Joseph Woosnam continued working at sea for both White Star and Cunard as a bedroom steward; in 1915 he married Ada Rose Owen (b. 1890) and with her raised a family. He died in Prescot, Lancashire in 1969.