I have turned UHMW using a skew chisel to make some parts for a swivel adapter on a vacuum chucking system. I prefer my oval skew for this because the included angle is around 40 degrees as opposed to the really fat angle (around 60 degrees) on my thick Lacer skew. As Steve and Al said, it wraps around the spindle/skew/tool post or whatever else is handy. Make sure that your skew is really sharp or you will just goober the stuff up. There is no smell like you might get from scraping some hard plastics, it just cuts like butter, but you can certainly dig in. And if you are a fan of the 80 grit gouge, just forget it. You will create a mess with a bunch of statically charged particles that will be permanently stuck to everything in sight – not to mention messing up the surface of whatever you are turning. If you need to fasten it to something else, drill holes and use screws.
Bill