You can't remove cut marks from laminate. Best you can do is disguise them. Invest in several good sized cutting boards so that you do not get any more of them. See if this helps.
Take a good photo to the paint department of the home improvement store and ask them what will work for you. They have the best selection, the most up-to-date materials and most important, the most informative sales staff to get you what you need for a professional job.