Carol is correct about the basic technique and results...when I was in 4th grade, (in an urban setting), I walked down the alley behind our house to the house where some kids we knew lived. The mother raised a few chickens in a little backyard pen, and was just planning supper.
Being only about 9, and being a city kid, I was not prepared for seeing her grab a hen by the head and do this motion like cranking an old car. Traumatic to a 9 year old....even more to the chicken.

I'd say it took 20-30 seconds before it quit flopping. I think an axe would not have bothered me.