One of the simplest floor care tools, a dust mop is a long-handled mop that is used to remove dust and small particles of debris from floors and hard-to-reach places like ceilings and walls. Also known as a dry mop, a dust mop is meant to be used dry, never wet.Many people wonder do you mop or vacuum first? Should you sweep before mopping? Mopping isn't a one-stop shop for cleaning the floors. You should always sweep, dust mop or vacuum to remove large pieces of debris and stray hair.