Cashmore was an aide to the general manager of the New York Edison Company and a furniture manufacturer.
He was a member of the New York State Assembly (Kings Co., 5th D.) in 1923. He was a member of the New York State Democratic Committee from 1938 to 1944. He was the Democratic candidate for U.S. Senator from New York in 1952, but was defeated by the incumbent Republican Irving M. Ives. He was a delegate to the 1948, 1952, 1956 and 1960 Democratic National Conventions.
Cashmore married Edythe Tenney (1898–1972). They had one son, James John Cashmore (1931–1977). The 1974 Harry Chapin song "Cat's in the Cradle" was based in part on John Cashmore's relationship with his son James, to whom Chapin's wife had been previously married.