Clean out the firebox, using a broom and dustpan. Don't leave any ashes or burnt wood inside the firebox. Open the damper, and close the glass doors or chain-curtain. Next, spread drop cloths over the hearth on your fireplace.
Roll a trash container into the room and place it next to the hearth. You will use the trash can to dispose of the broken flue tiles once they're removed.
Put on leather work gloves and a dust mask. Situate a ladder under the roof eve, and take a screw gun, cold chisel and claw hammer with you to the roof.
Walk over to the chimney, and unfasten the cap or top, using a screw gun. Unfasten the screen underneath the top, using the screw gun if applicable, and set both the cap and screen aside momentarily.
Hold the blade of the cold chisel between the chimney and the flue tile at a 30-degree angle. Tap the cold chisel with a hammer to break the flue tile away from the inside. Let the broken flue tile fall into the firebox.
Continue to break out other flue tiles as necessary, using the cold chisel and hammer until every flue tile has been broken away from inside the chimney.
Return to the inside of your house and approach the fireplace. Slowly open the glass doors or chain-curtain, and shovel out the broken flue tiles with a fireplace shovel, disposing of the pieces in the trash container. Sweep out the firebox again, using the broom and dustpan to make sure the area is entirely clean.