cat has punctured the wire

First you'll need to get a new power adapter as replacing the cable is not really doable.

As to why your cat chewed the cable it likely smells some food on the cord you transferred with your hands. You may want to get into the habit of washing down the cord with a good cleaner and to help teach the cat carefully wrap the cord with aluminum foil where the cat is likely to chew. Between the taste and the texture of the foil it should learn not to chew. As the foil is conductive don't cover your current cord as it could short and start a fire! Only do this on a good cord and don't get to close to the connector.