The son of Danylo Kardash and Ulyta Byck, he was educated at Hafford High School.
Kardash was a veteran of the Spanish Civil War, having fought with the Mackenzie-Papineau Battalion. He was a member of the Communist Party of Canada and, after 1943 the Labor-Progressive Party which was the legal front of the Communist Party after it was banned. Kardash became the first leader of the Manitoba LPP in 1943, and retained the position until 1948 when he resigned for health reasons. He was also the first national chairman of the LPP.
In 1940, Kardash married Mary Kostaniuk.
In 1941 he was elected to the provincial legislature in the ten-member district of Winnipeg and was re-elected in 1945. In 1949 and 1953, he was reelected in the four-member district of Winnipeg North. He was defeated in the 1958 general election, due in part to the pressures of the Cold War and due in part to the abolition of multi-member constituencies requiring him to contest a single-member seat for the first time.
The LPP's support base declined after 1945, and Kardash was the only candidate to run for the party in the Manitoba elections of 1953 and 1958. After his defeat, the LPP would never again elect a candidate to the legislature.
In 1948, Kardash became general manager of the People’s Co-operative Dairy, Fuel and Lumber Yards in 1948, retiring in 1982. He continued to served as president of the board of directors for the co-operative until the business was sold to its employees in 1993.
Kardash remained active in Winnipeg's Ukrainian community for the rest of his life. In 1995, he attended a public dedication ceremony at the Ontario legislature which honoured the veterans of the Mackenzie-Papineau Battalion.
After Kardash's death in 1997, the Manitoba legislature held a moment of silence in his honour.
- "MLA Biographies - Deceased". Legislative Assembly of Manitoba.
- "William Arthur Kardash (1912-1997)". Memorable Manitobans. Manitoba Historical Society.
- "Condolences made in the Manitoba legislature on the death of Bill Kardash (part way down the page)". Hansard. Legislative Assembly of Manitoba. June 26, 1997.