I will watch this post with interest! Shaving Tyres sounds like a really bad death metal band. My guess would be to blow the said tyre up really hard then somehow move it in to one of those ham slicing machines that they used to have in butchers shops.
Cutting tires is simple. Cut grooves in slicks all the time for supermoto. Always use a dedicated electric tire cutter, but the principle to take a few side knobs off a MTB tire is the same. Very sharp, very hot blade.
Stanley knife
Remember to cut TOWARDS yourself as this allows you the best control. Dont rush and dont use too much force. A sharp new blade which probably costs thruppence is a must and even consider swopping it (after turning it) for a new sharp blade after say doing 1/2 a tyre :?
When im cutting some veneers ,especially the bloody expensive stuff i will change the scalpel blade every 4 or 5 cuts.