Clarence Melvin Fines was born on August 16, 1905, in Darlingford, Manitoba, to Richard and Mabel (Willcott) Fines. He received his early education in Darlingford and in Stonewall. He attended Normal School in Regina, Saskatchewan, before attending the University of Manitoba and the University of Saskatchewan. He earned a Bachelor of Arts degree from the University of Manitoba via correspondence studies in 1942.
Prior to his entry into politics, Fines was a teacher and principal. He began his teaching career at Acreworth S.D. #3854 near Burstall in 1924. He later taught at Knox S.D. #826 and Cross S.D. #2188 near Riceton and at various schools in Regina. He was also principal of Strathcona School in Regina. Fines served as president of the Regina Teachers' Association (1937-1940) and as president of the Regina branch of the Saskatchewan Teachers' Federation (1941-1943).
Fines was a member of the Independent Labour Party and the Farmer-Labour Party before participating as a delegate at the organizing meeting of the Co-operative Commonwealth Federation (CCF) in 1932. Fines also served as an alderman for the City of Regina from 1934 to 1939 and from 1942 to 1944.
Fines was first elected to the Saskatchewan Legislature in 1944 as the CCF Member of the Legislative Assembly for the Regina City constituency. He was re-elected in 1948, 1952 and 1956. From 1944 to 1960, Fines served in the T.C. Douglas Government as Provincial Treasurer and as Deputy Premier. Ministerial responsibilities held by Fines from 1944 to 1960 included: Saskatchewan Liquor Board; Saskatchewan Government Purchasing Agency; Bureau of Publications; King's/Queen's Printer Office; Highway Traffic Board; Civil Service Commission; Farm Loan Board; and Provincial Auditor. Fines was also the Minister in Charge of Saskatchewan Government Insurance Office from 1948 to 1960.
Fines chose to not seek re-election in 1960. That year, he moved to the island of Grenada and worked as a corporate financial advisor for three years. He moved to Fort Lauderdale, Florida in 1963. In 1982, Fines' memoir The Impossible Dream: An Account of People and Events Leading to the First CCF Government, Saskatchewan, 1944 was published. Clarence Fines died in Fort Lauderdale on October 27, 1993.
Clarence Fines married Abigail Cox on January 13, 1926. They had two sons: Howard and Murray. He was later married to Lillianne Fines.