A break up, whether planned or a shock, cordial or full of conflict, is a significant event. It's not uncommon for men and women to make radical changes following a heartbreak. For some women, they cut their hair. Why?
Here are my speculations:
1) Stereotypically, men like women with long hair. If there's a desire to dissociate yourself from your ex and his preferences, chopping off your hair will make the statement, both to him and yourself.
2) Perhaps you've always wanted a new look but it wasn't preferred by your partner. Now you get to make the decision for yourself.
3) Look at yourself in the mirror. Short of changing out your wardrobe, your hair is an easy thing you can doing something about. A new hairstyle is not going to solve all of your problems, but it does give you some very visible control over your circumstances.
4) I'm often amazed at how fast my hair grows without me realizing. While that's not always the case for everyone, seeing new growth is also a reminder of the life possible after a break-up. Your hair will grow back, so your heart will also mend. If you keep the same style, growth is less noticeable.
If a new look is not enough to help you move on, let me know!