To dream of a separation, or being separated (or kept apart) from somebody, symbolizes a real-life situation or relationship that is breaking apart. Or, this dream may also mean indicates that your feelings are pulling you in opposite directions in a waking situation.... My Dream Interpretation
Seeing something that is whole divide into two parts equates to either a situational separation (such as in relationships), or purposefully separating your conscious self from a portion of subconscious awareness / feelings.
Separation into several sections may reveal your own multifaceted nature and parts of yourself that you are unwilling or unable to recognize consciously. This can also be an indicator of multiple personality disorder; however, any such serious malady should be professionally determined, not assumed or hypothesized.
Separating yourself from a person or situation in a dream is often a signal from your subconscious that you are actually ready to break those ties and venture out alone.... The Language of Dreams