Wedge a steel shovel under the lip of the driveway, on the encroaching side. To avoid injury from concrete shards, wear a hardhat, gloves, and safety glasses when breaking up concrete.
Ask a friend to hold the shovel for you to keep the edge of concrete elevated. This makes the job of breaking the concrete easier because it won't be supported by the ground underneath it. Your helper needs to wear safety gear as well.
Swing a sledgehammer down onto the lifted concrete several times to shatter it. Continue this until the encroaching area is in pieces. If it isn't breaking up effectively, nail a metal pick into the concrete and then hit the pick with a sledgehammer.
Scoop up the concrete remnants with the shovel and drop them into a wheelbarrow for later disposal.
Fill in the area where the driveway used to encroach with dirt and pack it in tightly with a shovel.
Clean up any broken concrete pieces on your existing driveway and then clean the area with a pressure washer.
Mix together a concrete repair compound according to package instructions. Pour the cement repair over the damaged driveway area and smooth it over the damaged section with a trowel. Spray the repair with water from a spray bottle every few hours. This aids the curing process.
Apply a resurfacer to the repaired area the next day using a rubber squeegee. This works best when the repair is slightly wet so use the spray bottle again before adding the resurfacer. Allow the repair to cure for another 24 hours before driving on it again.