Effects of the Crotalus adamanteus venom on mesentery of rabbit (top), and pectoralis of pigeon (bottom).
Many venomous snakes have hemotoxic venom, or a hemotoxic component within their venom. These toxins are able to break down red blood cells, disrupt clotting, and cause hemorrhaging due to the blood being thin enough to slip through capillary and tissue walls. Unlike a neurotoxic venom, which kills by paralyzing the diaphragm and suffocating the victim or prey, hemotoxic venom does not kill quickly. The internal bleeding and hemorrhaging of organs and major vessels is extremely painful.
When snakes kill with hemotoxins, they tend to follow their prey until it collapses, before attempting to eat it. However, the majority of the time, it turns out that the prey isn't dead yet. It's simply in shock and unable to continue - it would end up dying soon enough, but if the snake isn't too far behind it, the prey does get eaten alive.
Snake Venoms: An Investigation of Venomous Snakes, with Special Reference to the Phenomena of Their Venoms. By Hideyo Noguchi M. D., 1909.