Donagh was born in Dublin and went to school at Colaiste Mhuire. He joined the Abbey Theatre in 1981 two years after graduating as an engineer.

Donagh appeared in over 60 productions at The Abbey and Peacock including DA, HAMLET, THE PLOUGH AND THE STARS and EXECUTION. He later played in multiple productions at Red Kettle, The Passion Machine, Corcadorcha, and Poetry Ireland where he devised and directed shows on Joyce, Kavanagh and Beckett.

His TV and film work include GLENROE, FAIR CITY, ROS NA RÚN, and GAME OF THRONES.