Clear the room. Remove all furniture from the room. Pry off any moldings that sit on top of the vinyl composite tile.
Remove the old vinyl composite tiles with a floor scraper. Start on one side of the room. Slide the floor scraper under each tile with smooth, short strokes until the tile pops off of the floor. To lift stubborn floor tiles, place a putty knife between the floor and the tile. Tap the putty knife forward by tapping a hammer on the butt of the handle.
Put on your dust mask and rubber gloves. Open all of the windows in the room.
Remove the dried asphalt emulsion with an adhesive remover recommended by the asphalt emulsion adhesive's manufacturer. If you do not know or cannot contact the manufacturer, saturate the asphalt emulsion with mineral spirits until the asphalt emulsion softens. Scrape up the softened asphalt with a putty knife or floor scraper. Repeat as necessary to remove all of the asphalt emulsion.
Mop the substrate with a floor cleaner approved for use on that particular material. Follow with a fresh water mop to remove any traces of the cleaning solution. Towel or air-dry the floor.