How is stage makeup removed?

To understand removal you first need to know the application. The kabuki white face is not laid straight onto skin. A thin base of bintsuke pomade goes on first, and paste white is layered over it. That two-layer structure is the point.

The principle of removal is: take it off with oil. A heavily oiled cleanser is worked into the face, lifting the white and its pomade base together. What has been lifted is carefully wiped away, and only then is the face washed. One does not begin by scrubbing with soap and water: neither the white nor the oil comes off with water, so scrubbing merely spreads it and burdens the skin. The kumadori pigments are oil-based too, and come away the same way.

Applied with oil, removed with oil: the method of removal is built into the makeup itself. There is a secondary benefit. Because the pomade base forms a film between skin and pigment, little of the pigment is left on the skin when it comes off. Over long years this was presumably shaped into a method that holds up under daily repetition. Note too that before removal a face is sometimes pressed to paper or cloth to take an impression of the kumadori. This is oshiguma, kept as a memento — and only oil-based pigments make such an impression possible.