Pour a capful of mineral spirits into a rag to get the rag wet but not dripping.
Rub the wet cloth over the adhesive in circular motions until the mineral spirits dissolve the adhesive.
Scrape any remaining adhesive with a putty knife. This will not require much strength if the mineral spirit-covered rag had been wet enough to soak the adhesive without soaking the floor.
Wet the rag again with mineral spirits if the adhesive is difficult to remove with a few passes of the putty knife and rub the adhesive longer.
Wash the floor with warm, soapy water to remove mineral spirits before beginning the new floor placement.
Place a block of dry ice on the tile adhesive while wearing gloves to protect your hands from damage.
Allow the dry ice to freeze the adhesive for five minutes.
Place the dry ice on another section of adhesive and scrape the frozen adhesive off the floor with a putty knife. The adhesive should lift from the floor in frozen chunks after some strong scraping.
Continue this pattern until the entire floor is clear of adhesive.