Cassidy was born in Claremorris, County Mayo, Ireland. He received a Master's Degree in Applied Mathematics from Limerick University, and supported his early compositional activities with a day job as a statistician.
He is best known for his Narrative Cantatas—works he has written for Orchestra and Choir based on Irish Mythology. The Children of Lir released in September 1993 remained at number one in the Irish Classical Charts for a full year. It was the first Cantata ever written in the Irish language. The BBC later produced an hour long documentary on the piece.
Famine Remembrance, a commissioned piece to commemorate the 150th anniversary of the Irish Famine was premiered in New York's St. Patrick's Cathedral in 1996. A recording of the piece was released the following year.
Other albums include Cruit, arrangements of 17th- and 18th-century Irish harp music with Cassidy as the soloist and Deirdre of the Sorrows, another Cantata in the Irish language recorded with the London Symphony Orchestra and The Tallis Choir.