 Grassi was born in Chiasso.During his career, spent entirely in Switzerland and France, Grassi represented SC Zug, FC Chiasso, FC Zürich, Servette FC, Stade Rennais, AS Monaco, FC Sion, AS Cannes, Olympique Lyonnais and OGC Nice.At Monaco he was part of the side that won the 1996-97 Ligue 1 title, making 12 appearances in the process.