A backwards skill saw blade cuts almost anything a forward facing one won't! Sheet metal, tires, plastic sheeting, but hold onto it with two hands... I experimented with a tire tread as a soft edge for the my atv plow on a gravel driveway, so had to rip it all the way around. Surprisingly not tough enough, even with the steel belts, just chunks off.
Also an angle grinder works, cut out the sidewalls with utility knife, turn the tread inside out, zing through the belts, and finish with the knife.
I guess you could get all 8 tires into small chunks in not much time, but not worth $40 to most people, although I can't see how it would be bad in a landfill? It has so be sealed from the water table already?