The Berlin-based composer and percussionist, born in Thun in 1966, received his training at the Swiss Jazz School (1982–85), the Bern Academy of Arts (1986–90) and the Conservatory in Amsterdam (1991–92). He studied with Dieter Schnebel from 1995–99. Wertmüller was a percussionist in the Bern Symphony Orchestra and guested with the Concertgebouw Orkest, Amsterdam. 

His compositions are performed at Festivals like Donaueschinger Musiktagen, MaerzMusik, Lucerne Festival, musica viva, Ultraschall Festival, Akademie der Künste Berlin, Biennale Tel Aviv, JazzFest Berlin, Klangspuren Schwaz, Wien Modern, musique action Nancy, Huddersfield Contemporary Music Festival or London Jazz Festival. 

Hundreds of concerts with the band Alboth! and, since 2004, the trio Full Blast (with Peter Brötzmann and Marino Pliakas) have taken him to stages and festivals all over the world. Ongoing collaborations in various contexts with such authors as Dea Loher, Peter Weber, Michael Lentz, Reinhard Jirgl, Lukas Bärfuss and, in earlier times, Wolfgang Hilbig.

Wertmüller composed for Christoph Schlingensief and the Cologne Theatre, the Stuttgart Schauspiel and the Zurich Schauspielhaus. He has written two operas: Anschlag was premiered at the Lucerne Festival in 2013, and weine nicht, singe nicht at the Hamburg State Opera in 2015.