Born in Stuttgart, Mosch first studied school music at the Hochschule für Musik, Theater und Medien Hannover as well as German Studies and musicology at the University of Hannover and at Technische Universität Berlin with Carl Dahlhaus and Helga de la Motte-Haber.
1989 to 1990 he worked as an assistant at the State Institute for Music Research in Berlin.
There he was responsible for more than twenty-four estates and collections of music manuscripts and other documents of composers, including the collections of Igor Stravinsky, Luciano Berio, Hans Werner Henze, Helmut Lachenmann and Wolfgang Rihm as well as the collection of documentary films by Barrie Gavin.
In the winter semester 2014/15 he followed a call to the Université de Genève, where he heads the Department of Musicology.
Since 2017 he has been a member of the board of trustees of the Ernst von Siemens Music Foundation [de].