I gut them on the spot. As others have said, it doesn't seem to spook the other deer. With the scavengers we have here in East Tex, there is usually nothing left within one night!
Some places that I have hunted, don't want you to gut 'em in the field, so you would have to bring them back to camp to dress them out.
This is OK too, just that the hotter the weather, the sooner you need to get it to camp and dressed out.