Richard Mulcahy was born in Manor Street, Waterford, in 1886, the son of post office clerk Patrick Mulcahy and Elizabeth Slattery. He was educated at Mount Sion Christian Brothers School and later in Thurles, County Tipperary, where his father was the postmaster. One of his grandmothers was a Quaker who was disowned by her wealthy family for marrying a Catholic.
