Using a screwdriver or a drill bit that is the wrong size to try to extract screws can leave the screw heads badly stripped. Once stripped, even a screwdriver of the correct size likely won't help. Removing something screwed in with stripped screws--say, an old deadbolt lock--may require the assistance of a screw extractor.
Getting the stripped screws out of the old deadbolt lock (thereby removing the lock altogether) will require several items. You will want to obtain a center punch, a screw extractor, some titanium-coated drill bits, a hammer and a T-shaped twisting tool. Before you do any drilling or extracting, it may be wise to center-punch the stripped screws. Make sure your center-punch is made for metal. To perform the center-punch, simply place the point of the center-punch in the middle of a stripped screw and tap it forcefully with the hammer. This will create a depression, making it easy for you to place your drill bits securely there later. Do the same thing to the other stripped screws in the old deadbolt lock.
Once the screws have been prepared (thanks to the center-punch), use a 1/16-inch titanium-coated drill bit to drill a 1/16-inch hole into the center of the stripped screws. These are your preliminary holes (one in the center of each screw), but they aren't big enough yet. Use the drill bit with the next-largest diameter to increase the diameter of each of the holes. Repeat with larger bits, if necessary, until the holes are the same size as that recommended for the screw extractor (see instructions for your screw extractor). Make sure the screw extractor is about two thirds the diameter of the stripped screws in the old deadbolt lock. Now that holes have been drilled and widened to the appropriate width, the stripped screws are ready to be twisted out.
Actually getting the screws out is the easy part. Insert the screw extractor's tip into one of the holes, then gently tap it with the hammer. This should secure the extractor in place. Twist the extractor firmly into the hole counterclockwise, using the T-shaped twisting tool that should have come with the extractor. After a few moments, you will notice the screw begin to turn. Continue twisting and the screw will emerge. Now repeat this with the other stripped screws. As you are finishing with the final stripped screw, the old deadbolt lock should simply fall off.