Secure the power drill that contains the wood-plugged hole saw attachment to a level work surface. Use spring clamps or C-clamps. Adjust the clamps so that the hole saw attachment is just beyond an edge of the work surface and the power drill holding the plugged saw attachment is firmly attached to the work surface and its switch is off. Ensure thatthe power cord (if not a cordless drill or screwdriver) is unplugged from the power supply.
Drill one drywall screw about 1/4 inch into the wood plug approximately 1/8 inch from the edge of the stuck wood plug. Move to the opposite edge of the wood plug and drill in a second drywall screw similarly.
Return to the first drywall screw and continue drilling until you feel some resistance from the metal back of the hole saw. You should have about 1/2 inch of the drywall screw and its head protruding from the wood plug. Repeat the drilling for the second drywall screw and leave approximately the same 1/2 inch protruding distance on the second screw as with the first screw.
Choose either of the protruding drywall screws and continue drilling until the screw pushes on the metal back causing the stuck wood plug to begin to back out of the hole saw attachment.
Move to the other drywall screw and repeat the drilling process when the wood plug backs out about 1/4 inch, exposed to view. Drill until you again see the wood plug back out of the hole attachment exposing the wood and the screw. Move from screw to screw to back out the wood plug until it is almost out, say 1/4 inch from hole saw teeth edge.
Pull on the pliers to gently pull out the plug by the protruding drywall screws. Most of the the time you need only give a slight tug on one screw to remove the wood plug from the hole saw attachment. Discard the wood hole plug with drywall screws attached. Clean any wood debris from inside of your hole saw attachment in preparation for its use on your next hole project.