Mitchell was born in the County of Monaghan, Ireland. He and his three brothers were orphaned as young children after his father, William Mitchell, was reputedly killed in Dublin riots (his mother's cause and date of death is uncertain). The boys grew up in "Stackallen House" in County Meath, Republic of Ireland, the home of an uncle and under the care of a nurse. In 1810 he moved to live with his grandfather, Blayney Owen Mitchell, in Dublin who was a well-known attorney. While living there he was apprenticed to an apothecary for about one year and studied at Trinity College, Dublin before deciding to become a missionary.