To dream of a hard drive represents the accumulation of knowledge, beliefs, memories, or skills. Areas of your life that you have become adept at or experienced with. A cache of personal experience.
To dream of formatting may represent a major change to your belief system or priorities. You may be giving up old interests for new ones. It may also represent new developments that change everything you know. A major correction of some kind.
To dream of throwing out represents abandoning an area of your life. You are giving up something that you have a lot of experience with or that was of great interest to you.