This is in the part of the movie where the Grinch is preparing his Santa suit and getting ready for his thievery... "If I can't find a reindeer, I'll make one instead" - right after that. The Grinch puts a reindeer antler on the head of his dog Max, and ties it up with a black thread. He then finds that it is too heavy and Max's head droops to the floor. So the quick-thinking Grinch grabs a saw and starts cutting off parts of the antlers, so that it won't weigh down Max's head. Watch the part of the antler that goes behind Max's body as his head drops to the floor, and watch as the Grinch saws off pieces - that part behind his body never gets sawed off - but when Max pops back up (the lighter remaining antlers allowing him to do so), said antler portion is gone.