Her music has been described as "geometric post-jazz" (The Wire 302, April 2009) with such divergent inspirations as Charlie Parker and 1990s grunge music added a bit of electronica. As a composer she often explores the realm of graphic notations. In this special working technique she brings together visual art and music. 

In 2009 Laura Toxværd was awarded the prestigious three-year working scholarship by the Danish Arts Foundation. The scholarship was given as a joint award by the committees for classical and popular music. The committees wrote in their statement: 

"In her lively musicianship as a saxophonist, Laura Toxværd combines graphic score composition, improvisation, electronic components, and sound production in an integrated practice that communicates in an energetically insistent language. Toxværd’s musical nerve manages to encompass references, not only to odd corners of free jazz history, but also to machinery and animal noises in an expression ranging from cabaret-light to heavy-electronica - and all on an alto sax!"

Laura Toxværd got her musical education from the Rhythmic Music Conservatory in Copenhagen. During her studies she spent six months at Conservatoire Nationale Supérieur, Paris, and took classes with Barry Guy studying graphic notations. In addition she has earned a Master of Arts (philosophy of music education) from Aarhus University, Denmark. 

Her compositions have been released worldwide since 2002 on 15 audio albums (with i.a. John Tchicai), published internationally as graphic scores and in art books and performed in Europe and North America.

She has in recent years taught and examined at the Danish music conservatories and conducted artistic research as a lecturer at RMC, Cph.