Is it permitted to buy a vehicle and cut it into two pieces for parts, using only a single cut?

This depends entirely on your state's regulations around vehicle dismantling and title surrender, not on auction policy. Many states require a salvage or junk title to be surrendered to the DMV before a vehicle can be legally dismantled for parts, and some have specific rules about cutting vehicles for transport or parts purposes. Check with your state DMV or a licensed salvage yard before proceeding, since unauthorized dismantling can carry legal and title complications down the line.