How do you kill a zombie? The short answer is, destroy the brain. Whatever processes are working in the zombie; whether it's a living zombie or a modern zombie, whether it's undead or came back from the grave, however it's functioning, we know almost for certain if you destroy the brain you kill the zombie. If you must engage in combat with a zombie, however you can best accomplish destroying the brain is what you should do.
You want to avoid using a bladed weapon to cut off the head, because what that could potentially create is what we call 'land mines'. That is a zombie head lying in an obscure place; tall grass, weeds, obscured behind a piece of furniture, that's just sitting there lying and waiting for someone to walk by an get a bite on the foot or ankle, and you're a dead person. If you're really looking to inflict a lethal blow on a zombie, you want to focus all of your energy on destroying the brain however possible; whether that be a bludgeon weapon, a bladed weapon, a firearm, use a shotgun. However you can accomplish delivering a lethal blow to the head, that's what you need to do.