Insulation board is used to insulate walls and is typically found in basements or other buildings with concrete walls. Since it's made of foam, it resists moisture and mildew. Its low profile allows more overall floor space. If insulation board becomes damaged before drywall is installed, the insulation must be repaired to prevent moisture infiltration. Damaged insulation board also loses its insulation value.
Mark out a square or rectangular outline around the damaged portion of the insulation board. The damaged portion should lie fully inside the outline.
Cut along the marked lines with your utility knife. Push the knife progressively deeper with each stroke until you're all the way through the insulation board.
Remove the damaged portion of insulation board. If you can't pull it out, pry it out with a putty knife or pry bar.
Measure the opening you created, then cut a replacement piece using those measurements.
Apply construction adhesive to one side of the replacement insulation board. Push it into the opening with the adhesive facing toward the wall. Hold it in place for a few minutes to allow the adhesive to take hold.
Seal the seams with Tyvek tape. This completes the moisture and air barrier.
Use caution when cutting with a utility knife. The blade is extremely sharp and will cause serious injury when used improperly.