Depending on the area here in Colorado, the bucks will start stripping velvet sometime between the 10th and the 15th. Usually see all the bucks stripped out before the 20th.
When they are in velvet, their antlers are sensitive to being bumped with nerves extending up through the velvet along with the blood. When the velvet dies, the antlers are just bone and are not as sensitive to being bumped.
Their hormones change when the velvet dies. They seem to almost be sick or something for a week or so after they strip velvet and they tend to drop into thick cover and just do not move - at least during the daytime. They will leave the areas that they hung out in during the summer and drift toward where they will be rutting later in November or start moving down their migration corridors.
The food changes about the same time as they start stripping velvet. It is more pronounced up in the high country with the first real snows and hard freezes starting to hit about mid-September above treeline. In lower country, many of their food sources that they have been keyed in on have matured and started drying out.
If there is an early, big snow they will move down into the trees early. I have seen that happen on opening weekend where I hunt. If the weather clears after a couple of days, they will likely come back, but they will not go as high and will tend to hang right on the edge of the trees where they are harder to spot or stalk.
The buck groups will break up and the bigger bucks will go solo. The big boys get really hard to find then. The middle class bucks will still stay together, but more loosely.
If there is hunting pressure, they may disappear even in velvet. Our hunting season is only at the tail end of the cycle and mule deer antlers are already starting to harden.
Sometimes, you can get lucky and the bucks will stay in the same area that they have been in all summer after they strip out. They will just not move as much.
The toughest time to find and hunt mule deer effectively with a bow is that period when they are hard horned and not in the rut.
I tell people that the best time to hunt a mule deer buck above treeline is the first day of the season and it gets exponentially harder every day after that...
Treeline pretty much nailed it.