I'm going to have to agree with SLP here. This is pretty serious stuff, and as you're both new to the scene, it may not be something you should take on just yet. That said, because you are intrigued, I will leave you with my advice on safety. I've never done blood play or cutting of any sort, but I am in the medical field and hope that this will help you a little.
Small, shallow cuts will most likely not leave scars, but keep in mind, the deeper or wider the cut, the higher the risk of a scar. The sharper the knife, the thinner the cut.
I'm curious as to how much the two of you have looked into cutting, I'm hoping a good deal. He can't just pull out a knife and have at it.
One of the most important things to remember is to sterilize, sterilize, sterilize. Not only does the knife have to be clean (sterilized), but so does the area of skin that you will be playing with. Make sure you use an antiseptic when you begin, Betadine would work. Location is another consideration you will have to take. It sounds as though you're just talking about the breasts for now, but if you should ever experiment further, remember that the 'meaty' areas of your body are the generally the safest. Your breasts, your bottom, etc. Stay away from any area that is close to an artery and obviously, steer clear of areas where the blood vessels are close to the surface. You also should take into consideration diseases that you may be exposing yourself to. Gloves should be a must. I don't know how long you've been dating, but it is something you must consider. You should also be tied down, completely immobile. As you are new to this, you might accidentally flinch or jump while he is cutting. One wrong move could be the difference between an erotic scene and a trip to the ER.
He should go about this slowly, making precise and shallow cuts. This is not a scene to speed through. After making one cut, give it a few moments before moving on to the next. He
must be patient, slow and precise. This is a scene that could go wrong very quickly. When the cutting is finished, your skin will need to be cleaned (Betadine again) and the knife sanitized. If you're using razor blades, just throw it away and use a new one (sterilized) next time.
And of course, just in case something does go wrong, have the first aid kit handy - and stocked full of gauze pads and bandages!
I'm sorry if I'm coming off harsh, that is not my intent, I just want you to know what you're getting into so that you can go about it as safely as possible.