Matranga was born in Sicily and was the leader of the Matranga clan of San Diego. He was the son-in-law of Detroit mob figure Giovanni Priziola as was his brother Frank Matranga who was married to Priziola's other daughter. Joseph and his brothers Gaspar, Frank and Leo made up the nucleus of the San Diego crew of the L.A. family. Joe wielded tremendous influence in the area in which he operated along with members of the Los Angeles crime family and Chicago Outfit mainly through their representative Chris Petti. Much of Joe's influence was garnered from his family ties not only to Priziola but also to Salvatore Vitale another member of the Detroit mob with strong ties to the Sicilian mafia and an international drug smuggling ring.