Joseph was born and raised in West Hartford, Connecticut. He was blessed with a musical ability that seemed to guarantee a brilliant career as a classical musician, and he never considered an acting career until a music scholarship took him to the University of Miami, where a drama coach heard in Mascolo's hearty basso a voice that was destined for the stage.

Mascolo was first seen off-Broadway in a production of The Threepenny Opera, soon followed by an appearance in the landmark off-Broadway production of a View From the Bridge with director Ulu Grosbard, where he succeeded Robert Duvall as Eddie Carbone and joined an ensemble that included Jon Voight as co-star and Dustin Hoffman as assistant director. His Broadway debut came in Dinner at Eight, mounted by theatre legend Tyrone Guthrie.

Film roles include Sharkey's Machine, Heat, Jaws II, and Shaft's Big Score. His appearance in the film Yes, Giorgio! Gave him the opportunity to sing a duet with his friend, international super-tenor, Luciano Pavarotti.

The role of Stefano DiMera, which Mascolo portrayed on an off for almost two decades, garnered Mascolo with three Soap Opera Awards in the "Outstanding Villain" category.