I haven't gone into tire cutting detail here, as there are other Instructables that deal with this (eg auntwrenny, who thinks much the same as I do about leaving one sidewall on: http://www.instructables.com/id/Used-Tired-Raised-Garden-amp-Tree-Ring/
). I used a reciprocating saw for this step, but a sturdy sharp knife would probably do it with a lot more effort. A small amount of frequently applied water helps as a lubricant. Remember the proximity of electricity: if you kill yourself, don't say I didn't warn you.
Cut one sidewall from one tire and both walls from the other, leaving about a 75mm (3 inch) lip. I only cut out the upper wall of the second tire at first, but the polythene would not mould around the convoluted 3D-ness of this arrangement. Unfortunately, I did not take photos of the second try, but you'll get the idea.
Smaller tires can be done with a jigsaw or even a small knife: see the paring knife I used on car tires (thanks for the use Sweetie ... oh, I thought I'd asked you about that?... oh ... er ...).