How remove scratch off a diamond?

Although it IS possible for a diamond to be scratched, it's not very likely. It takes another diamond to do it, and it's difficult. If it's scratched it MIGHT not be a diamond. It might be, too, but it's odd that a diamond would be scratched. In any case it must be professionally repolished. There is no way for anyone without cutting equipment to do the job. And if it is a diamond only diamond grits will do the job, which few households even have. Go to a jewelry store and ask about it.