Can only do this with some 'unrefined foods' such as chicken, where you clean them (remove innards) but don't butcher it yet. So basically leave the bone it. Click it, then right click it onto the spit. Then turn to your hearts will. Enjoy your roasted chicken.
Chances are you cant for things like dear, bear ect that are large, I think its just to make things like chicken and rabbits last as a new in the world type thing, since dear bears ect produce enough meat to be fine