How does one effectively and quickly remove textured sand paint from plaster walls?

Don't know of any quick method. Especially if it really is sand that was mixed with the paint (and not just textured paint), you'll need to sand it smooth.

You could also skim coat the surface.

Both methods are time consuming and messy.

Depending on the room, consider using a Ralph Lauren textured paint - Suede or River Rock. These products are sold at Home Depots or call 1-800-379-POLO for other locations near you. You'd get a much nicer look than with a sand-based paint.

Good luck.