Set your polyurethane-stained suede shoes in a baking pan with the stains facing up. Place the pan in the freezer for two to three hours to freeze the polyurethane.
Remove the shoes from the freezer. Tap the frozen polyurethane with a plastic scraper to crack it.
Insert the edge of the scraper underneath the cracked polyurethane. Slowly wiggle the scraper back and forth to pry the pieces from the suede. Remove as much as possible. If the polyurethane softens, return the shoes to the freezer. Repeat Steps 1 through 3 to remove the hardened polyurethane.
Wear down remaining polyurethane by rubbing it with a nail file. Brush the dust off the suede shoes.
Rub the suede with an art gum eraser to remove residue from the surface of the shoes. Brush off any dust or residue from the polyurethane or eraser with your hands.
Moisten a clean cloth with white distilled vinegar. Blot the suede shoes at the site of the stain. Press another clean cloth into the surface to dry the shoes. Allow your shoes to air-dry completely.
Blend the nap by brushing your shoes with a suede brush.