Wait for the chimney to cool completely before cutting or installing the cleanout door. Place the door against the base of the chimney, 8 inches from the ground or floor. Trace the perimeter of the door frame onto the chimney with a pencil.
Drill holes on the inside of each corner with a 1/2-inch-diameter, 18-inch-long masonry bit and hammer drill. Drill holes on each side of the corner holes, 1 inch from the corner holes.
Continue drilling holes 1 inch apart one all four sides of the tracing. The 18-inch-long bit will drill through the masonry and the clay tile of the chimney liner.
Place the edge of a cold chisel between the space of two holes and tap the end of the chisel with a hammer. The chisel will bust through the masonry along the line between the holes. Continue chiseling through the spaces between the holes until the entire opening is cut out from the chimney. Dispose of the broken masonry and clay tiling as you work.
Mix mortar and water in a bucket according to the directions on the mortar bag. The consistency should be like a thick soup. Scoop some mortar on a trowel and place an even 1/4-inch layer on the bottom of the chimney opening.
Place another layer of mortar along the top flange of the cleanout door frame with the trowel. Insert the cleanout door into the opening until the door is flush against the chimney. Wedge a block of wood against the ground and center of the door to keep the door in place until the mortar cures.
Apply a 1/2-inch bead of heat-resistant caulk around the perimeter of the door and the chimney with a caulk gun once the mortar sets.