A lot of predators will do this because they want to get those calories in their bellies fast, before some other creatures come and chase them off. They'll ofte

A lot of predators will do this because they want to get those calories in their bellies fast, before some other creatures come and chase them off. They'll often eat certain organs first because of their high nutrient content. If the prey is dead or alive doesn't matter so long as it can't injure them or run off.