After beginning his career Off-Broadway at the Light Opera of Manhattan in the 1980s, Cuccioli starred as Lancelot du Lac in national tours of Camelot in 1987 and first appeared on Broadway in 1993 as Javert in Les Misérables.
He has appeared in numerous New York and regional productions since then, including his long-running stints on Broadway in Jekyll & Hyde (1997–1999) and as the Green Goblin in Spider-Man: Turn Off the Dark (2012–2014).
Cuccioli returned to Broadway beginning August 7, 2012, when he took over from Patrick Page in the dual role of Norman Osborn and his alter ego The Green Goblin in the rock musical Spider-Man: Turn Off the Dark.
[4] Aside from Cuccioli's early tenure at the Light Opera of Manhattan, his other notable off-Broadway appearances include Nathan in the long-running revival of The Rothschilds (1990); the highly successful 1991 Kander and Ebb revue And The World Goes 'Round, which garnered him an Outer Critics Circle Award in 1991; and he played the title role in the Maury Yeston and Arthur Kopit musical Phantom at the Westchester Broadway Theater in 1992–93, a role that he has repeated.
[6] Cuccioli's U.S. regional theatre credits include Ankles Aweigh at the Goodspeed Opera House in 1988, Jud Fry in Oklahoma!
Later that year he played the title character in Man of La Mancha at the White Plains, New York Performing Arts Center.
[9] In 2008, he returned to the White Plains Performing Arts Center to play King Arthur in Camelot and starred in Conor McPherson's The Seafarer at George Street Playhouse in New Jersey.
[13] In 2019, he played the title role in Caesar and Cleopatra in off-Broadway's Theatre Row Building in a production by The Gingold Theatrical Group.
He has appeared in several films, including in Woody Allen's Celebrity (1998), Operation Delta Force 3: Clear Target (1999), Heroic Times and The Stranger.