It is completely safe to use Neosporin, also called triple antibiotic ointment, on a dog. As long as the dog's cut or abrasion isn't too deep, Neosporin can help to prevent infection and possibly decrease healing time.
Neosporin contains antibiotics that help to reduce the risk of infection from open wounds. A dog that has a puncture wound or a wound that won't stop bleeding should be seen by a veterinarian before applying any antibiotic ointment. Neosporin is meant for external use on the skin only, so dog owners should not use the ointment for eye or mouth wounds or infections.