Donal Francis Logue was born in Ottawa, Ontario, to Irish parents from County Kerry. His parents were Carmelite missionaries, and the family moved from Ireland to Canada to Boston and elsewhere before settling in Calexico, California, in the state's Imperial Valley. There and in nearby El Centro, California, Logue grew up with three sisters—Karina, Deirdre and Eileen—and their mother taught at Calexico High School and Vincent Memorial Catholic High School. Logue attended Central Union High School in El Centro, where he became interested in theater. With friend John Everly during what Logue called the "summer during our sophomore year", he created the theater group Imperial Valley Players to perform in the school's auditorium, mounting the theater of the absurd play Picnic on the Battlefield by Fernando Arrabal.
For part of his junior year of high school, Logue attended the Jesuit school St. Ignatius' College in Enfield Town, London, England. In 1983, while a high-school senior, Donal was elected president of the 37th session of the American Legion Boys Nation, representing California and becoming the first non-citizen elected Boys Nation president. He went on to study history at Harvard University, graduating in 1988. In the late 1980s, he worked as a road manager for such bands as Bullet LaVolta.