The only way to complete destroy a zombie is to crush its entire head. Otherwise the disassembled parts will still try and reanimate themselves...
Per Monster Hunter International, the preiminent monster erradication company on the planet:
There are many different variations of undead, with your basic zombie being the simplest of all. A zombie is just an animated corpse, wandering around in search of one thing: flesh. The big problem with zombies is that they multiply like rabbits. Their bites are always eventually fatal, and the bitten always rise as zombies themselves. Their poison travels instantly through the nervous system, and not even amputation of the bitten limb can stop the transformation. Basically, they're a major pain in the ass, the Monster Hunter's equivalent to cockroaches. Usually stupid, and normally slow, zombies are not much of a challenge for an experienced Hunter, provided that said Hunter has a decent gun and friends with guns.