Adamo was born in Alcamo, Sicily. Adamo and his brother Girolamo "Momo" Adamo both immigrated to the U.S. and became members of the Los Angeles crime family. Momo became the underboss of the family under crime boss Jack Dragna. When Dragna died in 1956, Frank DeSimone became the new boss and demoted Momo. After this both brothers relocated their base of operations to San Diego where they became closely associated with the Matranga and LiMandri family's. In San Diego, Joe was a soldier in the crew of "Papa Tony" Anthony Mirabile and upon Mirabile's murder in 1958 became the capo of the Los Angeles family's San Diego faction.
Adamo participated in the murder of fellow L.A. family mobster Frank Borgia, who was killed for refusing to share his illicit gains with the Los Angeles family, Adamo reportedly helped to dispose of Borgia's body. The murder was carried out at Adamo's home in San Diego. Adamo owned the Panama and Arizona clubs in San Diego along with an interest in various bars and clubs. The Federal Government once tried to deport Adamo as both he and his brother had entered the country illegally but the deportation order against Adamo was eventually thrown out.
He remained in the U.S. until his death of natural causes in the 1970s.