Traditionally, I think vampires have to have wooden stake through the heart, or sunlight, or holy water, or have their head severed and buried on hallowed ground and stuffed with garlic or some such thing.
Normal injuries don't phase them. Though it would be fun to have one accumulate damage but still be alive. Or maybe they survive but only heal very slowly. So a vampire running, or hey, crawling around with a floppy, broken neck for a while.
But it's your story, and there have been enough liberties with vampire lore over the years that as long as you give them a believable Achilles heel (with maybe a nod to the misconception or myth that they can only be killed in the above ways), you can have them be vulnerable to whatever you want them to. It's your universe.