Drive two to three wooden wedges a few inches between the stable stones surrounding the popped stone. This will take some of the weight off the popped stone.
Remove the popped stone out of the rock wall by carefully working it out with your hands. Try to refrain from dislodging other stones while working the popped stone out.
Drive the wedges a few more inches into the wall with a rubber mallet. Place the popped stone back into the empty cavity.
Place a 2-by-4 that is covered with carpet against the popped stone and gently tap the 2-by-4 with a rubber mallet until the stone is back in its proper place. Remove the wedges from between the stones.
Chisel the mortar around the damage stone with a chisel angled in the direction of the damaged stone. This will prevent additional damage to the surrounding stones.
Pry the damaged stone out of the rock wall. Remove the remaining mortar in the cavity with a wider cold chisel. Brush the debris out of the cavity with a soft-bristle brush.
Place the new stone, which is slightly larger than the cavity, against the rock wall. Use a marker to create the cut lines on the new stone that corresponds with the shape of the cavity.
Attach a masonry blade to a circular saw. Cut the new stone according to the shape, size and width of the cavity with a circular saw.
Use a mason’s hammer to chip away at the new stone until it will fit into the empty cavity. When chipping the new stone, provide enough space to add mortar joints.
Fill a spray bottle with water and mist the inside of the empty cavity. Spread an even layer of mortar on the cavity’s bottom. Spread the mortar on the sides and top of the new stone.
Place the new stone in the empty cavity, using a pointing trowel to push it into the correct position. Pack the mortar against the sides of the stone and allow to set.
Chip the damaged mortar out of the wall using a thin cold chisel and rubber mallet. Brush the joint with a soft-bristle brush. Continue in this manner until you reach solid joint mortar.
Mix the mortar according to the manufacturer’s mixing instructions for use in a mortar bag. Fill the mortar bag with mortar.
Dampen the joint with a spray bottle filled with water. Apply the new mortar to the joints by squeezing the mortar out of the bag and over the damaged area.
Pack the joint with a pointing trowel. Continue adding mortar if needed and packing it tightly with the trowel until the damaged joint is filled. Let the mortar set.
Pour a small amount of liquid waterproof membrane in a paint tray. Use a waterproof membrane safe for use on rock and stone walls.
Secure a clean rolling nap on a paint roller. Roll the nap in the paint tray until it is covered with the waterproofing. Alternatively, use a large, clean paintbrush.
Start rolling the liquid waterproof membrane on the back of the rock wall. Continue rolling the liquid in an even back-and-forth motion while moving toward the opposite end of the stone wall until the entire back of the wall is covered.
Let the waterproof membrane cure for the recommending time frame as stated on the specific application instructions located on the back of the bottle.