There a variety of short choppy hairstyles, some of which are punk rock. A variation is the asymmetrical spikes. You don't have to be a boy to do that. Cut the hair in short lengths, and optionally have bangs at the front of your face. Hold some hairspray, and spike your hair up. Get layers which are longer in the front and shorter at the back, to make it easier to spike them more and try some variations.
If you are not in the punk rock style, and want to start with the basics, then the short chop would be a good style for you. It is not very choppy in terms of layers and sections though. The back of the hair has great texture and separation which shows a choppy look. The front is neatly parted to one side through the centre. This maybe lightly chopped, but a good short choppy hairstyle.If you are a young woman looking for a wild and rough look, then choppy messy hair are for you. The bangs at the front are brushed to cover the forehead, and graduated layers provide definition to the cut. The added volume and covering bangs provide enough details to be fitting for any face shape. A nice choppy short hairstyles.