Tassie was born in Pollokshaws, Glasgow. He trained first as a stone mason and then attended the Foulis Academy in Glasgow. Tassie moved to Dublin in 1763, where he learned how to make imitations of antique cameos. He invented a formula for a type of glass paste which he used for the rest of his life to make gems and portrait medallions. Tassie moved to London in 1766. His reproductions of antique gems were avidly collected by patrons as distinguished as Catherine the Great of Russia. He was also the leading portrait modeller in Britain, making around five hundred medallions of his contemporaries.