Higher durometer polymer foams- EVA, extruded polystyrene, rigid polyurethane (tooling board), polyethylene (Kaizan), etc- are perfectly fine to machine and can even be done so at relatively low RPM. Foam rubbers, or low-durometer elasticized foams, are highly likely to deflect, deform, and grab the bit, which could lead to a stall or a crash. They're generally cut with a hot knife or hot wire, or cast to final form in a rigid mold.
Depends how large and depends what they're gonna be used for, but in general EVA floor mats would work just fine, stacked and contact cemented (ideally Barge, but some people get good results out of Weldwood too) together. With EVA's raw edges, even after heat sealing I'd still run some kind of spray or brush on coating around the outside to add density too. Ideally something specifically intended for the job, like Creature Cast semi-rigid neoprene rubber - 1 pint 'Semi-Rigid' Creature Cast Liquid Rubber (Black) — Creature Cast Rubber (might need the Neo-Thix or whatever they call it for this app too) - but something like Rustoleum "Rubberized Undercoating" (I think that's what they call it, big can, sprays pretty nicely) would probably work in a couple of layers too. You'd have to do some testing to see how well the detail holds up and if you need to machine away "extra" for the coating to fill in, though. Personally I'd machine or print (which has been done before for tyres, I've seen it) negative molds and then slush cast in something like Creature Cast, without the thickener, and backfill with a more rigid foam or even solid urethane (to precisely locate the axles). I dunno, lots of options, but you gotta know about them first.
I'm new to Openbuilds, but have been in the rubber industry for 35 years. "Cutting" is not the way to go. Grinding is. If there is a thin Rasp-Like tool, that should work well. An air stream and vacuum to remove debris would be recommended.
That is how I would make kayak seats out of foam. I would carve it until it fit my butt properly. Recently, I cut the gray floor tiles with the laser. That was super easy. But, you need a laser.
I wonder if composite cutters would fit the bill- they're very rasp-like. I still can't imagine it working too well for making a 3D shape like a tyre without a 4th axis vs a more traditional method like molding, but for the price of one cutter it could be worth a try.
