There are some punk/hard-rock bands that have attempted playing classical pieces. For example
Scatterbrain released a stunningly good version of
Mozart's
Sonata Number 3. It's on their album
Here Comes Trouble, and it's also on an
Australian single they released including a live version where the vocalist blames a guy in the crowd for stuffing up the guitarist's solo.
It's mad, it's frantic and it works.
Thanks to Segnbora-t for the suggestions and corrections.