Ummm, I am not a doctor, so if it is pretty bad / bothers you a lot, I would go ask a real doctor.
My thoughts are that these "cuts" are probably skin tears, either from being too far stretched out or from the air being dry where you live, or from too much friction etc. These happen all over your skin from time to time and usually heal pretty quickly. Make sure you're using lots of lube (even though it sounds like you already are) and that you try to keep your penis moisturized when you're not masturbating, maybe? I honestly don't know what to tell you on this one.