Davidson was born in 1923 in Yonkers, New York to Jewish parents. He served as a Navy hospital corpsman (medic) with the Marine Corps in the Pacific during World War II, and began his writing career as a Talmudic scholar around 1950. As reported at the time in the February 20, 1962 Yonkers daily, the Herald Statesman, Rabbi Arnold Weinberger officiated at his wedding to Miss Grania Kalman, which took place at the home of Damon Knight.
This made his conversion to Tenrikyo in the 1970s unexpected. Although he had a reputation for being quick to anger, Davidson was known among his friends for his generosity. His peripatetic life and career may have been due to a disinclination to finish what he began. His reputation among science fiction and fantasy readers peaked in the 1960s, after which he had a coterie of fans who (as with R. A. Lafferty), kept his reputation alive, especially after his death.
He was a member of the Swordsmen and Sorcerers' Guild of America (SAGA), a loose-knit group of Heroic Fantasy authors founded in the 1960s, some of whose works were anthologized in Lin Carter's Flashing Swords! anthologies.
While editing The Magazine of Fantasy and Science Fiction he lived in Mexico, and later in British Honduras (now renamed Belize). He lived in a rural district of Novato, in northern Marin County, California, in 1970, but later moved closer to San Francisco. He lived in a small house in Sausalito, at the southern end of Marin County next to San Francisco in 1971 and 1972, and it was there fans and friends were welcomed. He worked for a short time in the late 1970s as a creative writing instructor at the University of Texas at El Paso. In his later years, he lived in Washington state, including a brief stay in the Veterans' Home in Bremerton. He died in his tiny apartment in Bremerton on May 8, 1993, aged 70. A memorial service was held in Gasworks Park in Seattle.
He was survived by his son Ethan and his ex-wife Grania Davis, who continued to edit and release his unpublished works until her own death.