In 1956 he reached the summit of Monte Sarmiento in Tierra del Fuego and in 1958, as a member of Riccardo Cassin’s expedition in Karakorum, he and Walter Bonatti made the first ascent of Gasherbrum IV (7,925 m).
Mauri je kot alpinist opravil več prvenstvenih vzponov v Alpah, med katerimi je prvi zimski vzpon po smeri "via Comici" na Cima Grande di Lavaredo ter prvi solo vzpon po smeri "Poire" na Mont Blanc.