Most of time when a mammalian predator consumes it licks up the blood as it goes. Raptors often kill causing blood flow to stop before they consume which means very little blood. I have seen many animal kills on chickens, likely more than most, and have taken time to not only document kills...
Large bird being left behind as a headless and neckless carcass caused by predator not trying to pack it off. Such generally rules out a coyote or bobcat but can be very consistent with a fox or raptor. I would leave the carcass out, possibly tying it down and seeing who comes in. My bet is...