How soon after the shot did you gut your deer. It may have been nerves still firing and causing the intestines to do what they do, Peristalsis. Many body systems do not stop functioning immediately upon death. Humans will often evacuate their bowels some time after actual death. No reason a deer will not do the same.
"Government is not reason; it is not eloquent; it is force. Like fire, it is a dangerous servant and a fearful master."