I'd think just twisting the head, very hard, would be enough for a dove. Birds have little skinny necks. Biting it off might expose you to all kinds of bacteria and parasites.
I really wish I had a video of my great-uncle the chicken farmer wringing the necks of two chickens at once.
I really wish I had a video of my great-uncle the chicken farmer wringing the necks of two chickens at once.