Cutting releases endorphin's and gives people an adrenaline rush and false sense of euphoria. Unfortunately it is short lived and can become an addiction (much like drugs). The best way to overcome it is to find the true reason why you are cutting and deal with it head on. Find other methods for gaining the euphoria. (Exercise for example). But truly a person has to learn to deal with their inner demons.
I used to cut myself when I was a freshman in college. I suffered from depression and anxiety most of my life, and it seemed like the only thing that would make me feel better. Then I got smarter and learned how to cope with things in a better way by taking care of myself vs. harming myself. It took a lot of years. I don't like the physical scars it left, but I use them as a reminder of where I was then compared to where I am now. So I can't honestly say I don't regret it, but I would never advise someone to do it.