Remove the screws from the saw. Place the screws inside an empty cup and place the saw handle on a safe surface.
Scrape off the residue that is on both sides of the saw blade, using a single-edged razor blade. At a low angle, gently scrape the dirt, wax, oil, or whatever else is caked on the the saw blade. Scrape the residue away carefully to avoid scraping the surface of the saw. Once you remove the residue, place the it into a trash can or container that you can toss (such as an empty coffee can).
Put an air mask over your face, and put on some work gloves. Gently open the container of mineral spirits then pour the mineral spirits in small amounts on both sides of the blade.
Take a square of sandpaper and sand the blade parallel to the length of the saw blade. Once you remove all of the loose residue, take a few sheets of paper towels and wipe off the mineral spirits from the blade. Dispose of the paper towels in a non-flamable area (these paper towels can burn easily). Once this side of the blade is dry, repeat Steps 3 and 4 for the other side of the blade.
Take your razor blade and remove the dirt and grime from the handle of the saw. Once you remove it, use a piece of steel wool and scrape the wood handle until you remove all of the residue from the handle After you finish with the handle, wipe off the saw and the handle with a rag to remove all of the mineral spirits and grime from the handle and the saw. Your saw and handle are now clean and tarnish-free.