IMPO, just about any alternative has to be better than the pain of cutting a tire in half not to mention the possibility of exposing wires that someone or some animal could get cut on.
You could put a couple bolts near the edges of the halves and sink them into some concrete but you probably don't want concrete there either... use anchors (maybe bend rebar into long "U" shape and hold them down via the bolts, driven into hard ground, but at some point it's going to get tipped over and then I agree with 2manyrocks above, don't want that exposed metal out where jumping goats are goofing off.
Backwards blade on the skill saw didn't have much too trouble cutting a car tire all the way around through the steel belts. Just hold onto it tight with two hands. Having some wooden wedges handy would help keep the cut open.
Cut the steel cable in the bead with an angle grinder. After that a sharp knife will cut across the tread. Or continue with the angle grinder, just wear a mask to protect from the rubber dust. If you must use multiple tools then any wood cutting blade will do the tread and sidewalls.