Protect your surrounding work area before you begin working. Place drop cloths over any furniture that cannot be easily moved. Place a 1/2-inch or thicker sheet of plywood across the hearth extension if you have one.
Connect an exhaust fan on the top of the chimney. Removal of the firebox is likely to create a considerable amount of dust and smoke that you can remove by using an exhaust fan at the top.
Remove any trim or framing around the firebox if necessary.
Remove or cut the fastenings that hold the firebox in place if possible. If you are able to easily remove the fastenings, you should be able to pull the firebox directly out in one piece.
Remove the damper if you are unable to get the firebox out in one piece. Cut the pins at each end with a Sawzall. Once the damper is removed, be sure to vacuum the smoke shelf with a shop vac and then stuff the heatform channels with fiberglass and tape the front of the damper closed with duct tape.
Create cuts in the firebox by starting in an upper corner and cutting down to the floor of the fireplace. Make a similar cut in the other corner. Continue making cuts by cutting horizontally across the firebox just below the damper and again a few inches from the floor. Remove each piece as you cut until you've removed the entire firebox.