I could never decapitate an animal that I cared for as I know it is a painful way to die, I have pet turtles, 2 of whom, if left to nature would be dead now as one doesn't have a hinge (very important to box turtles) and the other is walleyed... If it came down to having to put an pet down I would give it medicine to put it down. Then again I raise animals to be part of my family, not livestock.
If you're raising them for food or selling, I can understand culling the sick and weak, but if raised for pets I cannot understand. Mashed up pain pills would be more humane than decapitation in my opinion though, as the brain is alive for a few seconds afterward most likely in a state of shock but I digress... A bullet to the brain would be less painful, since the brain would be destroyed less than a second after firing.
Not trying to be judgmental of anyone, since what works for me might not work for you, just writing how I feel about the subject.