Mulcahy, Jeremiah Hodges, artist and art teacher, was born in Limerick on 15 September 1804, the son of Ellen Sheehan and James Mulcahy. His early life is shrouded in mystery, but it is thought his parents came from Cork, where they were married at St Peter and Paul's church in 1802. In his teenage years he attended an art school in Limerick and received tuition from Morris O'Connor. An exhibition was held there in 1819 or 1822 showing the work of the pupils and works of the great masters on loan from local art collections.

Mulcahy is regarded as a regional artist rather than one of Ireland's outstanding painters. Landscape works dominated his oeuvre and are, in the main, noteworthy for their content and topographical importance. He was inspired by the styles of seventeenth- and eighteenth-century landscape artists and also by the ideals of the Romantic movement. In his early years, from the 1830s onwards, he received patronage from many of the gentry and aristocracy of Munster. In 1839 Mulcahy became a member of the Freemasons of Ireland at Eden Lodge in Limerick, enabling him to develop connections, friends, and potential patrons.

Mulcahy exhibited at the RHA from 1843 until 1878. In 1861 he was proposed for election as a member at the annual meeting of the RHA, his opponent being the English-based artist Francis Danby, who was the more prominent of the two. Mulcahy was defeated by one vote. Danby died in the same year, and Mulcahy began his battle for recognition among his fellow artists. He exhibited extensively in Ireland at Cork, Dublin, and Limerick, notably at the art union exhibitions and the great industrial exhibitions of Cork and Dublin.

Mulcahy died 25 December 1889 at his home, at 11 Avondale Terrace, Harold's Cross, Dublin, and was buried in the family vault at St John's church, St John's Square, Limerick.