How Painful is Beheading/Decapitation?

My grandfather was in WW2 ,not sure where he was stationed ,but im pretty sure wasnt Germany . Anyway when my grandpa was alive he use to tell us storys of being over there ,and how it was. Told me a story one time of watching a man be beheaded ,and how the man ran around without a head for a few moments before falling. I believe even without a head it takes your heart a few moments to realize ,and it does still beat .