Drill holes through the mortar surrounding the brick you wish to cut using a drill with a masonry bit attached. Place the holes about 1/2 inch apart, to the depth of the base of the brick. Place the tip of a chisel over the remaining lines of mortar between the holes and strike with a hammer to cut the lines through to the brick base, creating an opening surrounding the brick and isolating it from the other bricks in the fireplace. The isolation will ensure that no other bricks are cracked when cutting the desired brick due to shocks from the cut traveling to the surrounding bricks.
Use a piece of chalk to mark a cutting line across the brick. Place a speed square on the face of the brick to help you make a straight line with the chalk where desired.
Score the chalk line with the edge of the chisel and then place the tip of the chisel onto the scored line. Angle the chisel slightly, about 60 degrees with the tip aimed at the portion of the brick you plan to remove. Hit the chisel lightly with the hammer, cutting a shallow line along the chalk about 1/16 inch in depth. The shallow cut lowers the amount of force needed to cut the brick with the brick set.
Position a brick set blade in the shallow line. Turn the blade so that the beveled edge is against the part of the brick you’re removing. Angle it slightly toward the removable piece and then strike the head of the brick set with the hammer with a clean firm stroke. The set should cut through the brick to the base without disturbing the surrounding bricks
Place a flat prybar into the joint adjacent to the removable portion of the brick and then apply upward pressure to pop the brick from the surface of the fireplace.
Use the hammer and chisel to remove any chips remaining on the edge of the portion of the brick still attached to the fireplace surface.