If the damaged wall has more than one hole in it, it is better to replace the entire drywall sheet than to replace a section. This will give more structural integrity to the wall, as well as hide any seams.
Check your blueprints to make sure there are no electrical wires running behind the area being cut. If there are, don’t cut too deep with the drywall knife.
For small holes, just use the mud and mesh method instead of cutting out the drywall.
After applying joint compound, use mesh tape versus drywall tape to cover the seams. It is harder to conceal a seam with tape. Plus, mesh creates a stronger bond between the old and existing drywall pieces.