author did the homework, nice. the fact that mr smith wonder why theres no much blood actually confirm author understands it. by slicing the throat correctly, almost all the blood will be pumped out before the animal actually died, so the meat will be cleaner when they cut it after that.
and no, its not to make them suffer too, since you need to cut its flow of oxygen to the brain in the same stroke. so the brain goes into some kind of shock and confusion state(you cant think clearly what happening without oxygen in your brain) and thus making the heart pumped blood faster resulting in faster bleeding