Born in Draguć (Draguccio d'Istria) by Buzet (Pinguente) Istria, Grossich at first studied law in Graz, but then shifted to medicine in Vienna, graduating in 1875. At first (1876–1878) he worked as a physician in Kastav, close to Fiume. Antonio Grossich was mobilised and took part in the Austrian campaign in Bosnia in 1878, serving in the Austrian army as "Oberarzt". In 1879 he came to Fiume, and in 1884 he went back to Vienna to specialize surgery and obstetrical medicine. There he worked at the First Surgery Clinic of the University of Vienna with Karel Maydl. He practiced obstetrical medicine under the supervision of Eduard Albert, who from 1873 to 1881 was a professor of surgery in Innsbruck, where he introduced mandatory antiseptic treatment for wounds. In 1886, he became Chief of the Surgery Division at the City Hospital of Fiume. Grossich was among the first to use sterilisation of the operative field and in 1908 tincture of iodine was introduced by Grossich as a way for rapid sterilization of the human skin in the surgical field. It was tested on a mass level during the Italo-Turkish War of 1912. For this reason he was awarded with the Order of the Crown of Italy, and become a surgeon. Grossich became involved in the political life of the city, taking an Italian irredentist stance, eventually becoming the head of the Italian National Council of Fiume in 1918. In 1924 he consigned the Key to the City to the Italian king Victor Emmanuel III on the day of the official annexation of Fiume to Italy, where he later died.