If you dream of cutting off your hair, it might mean you are undergoing change. You may be shedding a more aesthetically pleasing image, in exchange for a transformation. You desire a change to emphasize the making of a new you. If you did not initiate change in your waking life, then this dream is a reminder hoping to spur you into action.
The dream symbolism of cutting off hair also refers to the shedding of a weight. Your brain tells you to get rid of the chore and its related responsibility of taking care of it. The imagery of hair is symbolic. It stands for the burden you are currently shouldering. You may be having a heavy load on your shoulders and hence, your inner consciousness created this dream, to try to offer you some relief.