The vibration usually loosens roots adhering to the container's walls. Next, tap the upside-down pot on the bench edge to free the root mass completely. Last spring, I broke a kitchen knife attempting to divide one big clump of a standard hybrid. With some care, use a sharp clean saw to divide massed pseudobulbs and roots without damaging active growths. Take steps to prevent the spread of virus.
Flame sterilize the saw first, and then again before separating a new division.
To flame-sterilize, pass the blade through the flame of a gas stove. If many cuts will be made, it may be beneficial to invest in a portable propane torch that clips on to a replaceable fuel cylinder. Active small divisions or seedlings can be gently moved to larger containers anytime. However, disturbing all of the roots and dividing clumps is safest during the warmer spring and summer months. Once separated into easily handled units, pull off old leafless pseudobulbs and pot separately.