Since dogs are constantly running, and on there feet, a cut on a pad is very difficult to heal. Peroxide for cleaning is fine. If you take your dog to the vet, you'll have a hundred dollar bill and nothing can be done. Buy a tube of super glue and put three coats of super glue over the cut. Do you have a muzzle? Before you put it on, you need to find a way to prevent the dog from licking it off. It only takes a minute for the super glue to dry totally, and this will give your dog a protective cover over the pad that will last awhile and will allow it to heal completely.
Rinse it with some hydrogen peroxide and put some neosporin on it until it gets better. Don't let your dog lick it off, that could only make it worse.