To provide a sheet take-out apparatus for preventing double feed of sheets and controlling gaps to a desired value, a sheet processing apparatus, and a sheet take-out method. A take-out apparatus includes a supply structure for supplying postal matter to a take-out position, a take-out structure for taking out the postal matter from the take-out position, and a conveying structure for receiving and conveying the postal matter taken out on a conveying path. When a leading edge of the postal matter is held by the conveying structure, an absorbing operation of a vacuum pump is stopped and a moving speed of a take-out belt is reduced. Furthermore, when the postal matter is detected by a sensor, the take-out belt is stopped.