Mallet was born in Dublin, the son of Robert Mallet, a geologist. After studying at the Enniskillen Royal School in 1858 he joined the Geological Survey of India in February 1859. He worked in the Himalayas, Central India, Assam and Burma while also being in charge of the Museum and Laboratory. He published numerous papers on the geology of the Vindhya range and examined the Barren Island volcano. He became a Superintendent of the Survey in 1883 and retired in 1889. He contributed to Medlicott's Manual of the Geology of India, the fourth part which dealt with mineralogy. Mallet was involved in the survey of coalfields in the Naga Hills, the Son Valley, southern Mirzapur, and Rewa. He accompanied Ferdinand Stoliczka and William Theobald on expeditions to the Sutlej and Spiti valleys. He was the first geologist to scientifically study the Ramgarh crater in 1869.