An asynchronous transfer mode (ATM) switching system includes a cell switching assembly having at least one switch port for transferring an ATM cell, and a subscriber board having a plurality of subscriber ports. A cell processing apparatus for use in the ATM switching system includes a look-up memory for storing control information for determining whether to copy an ATM cell from the switch port, and a cell copy controller for copying the ATM cell from the switch port and transferring ATM cells copied to the subscriber ports according to the control information stored in the look-up memory. If the ATM cell is a point-to-point communication cell, the ATM switching system translates the header included in the cell according to control information and transfers the ATM cell having the translated header to at least one of the subscriber ports. However, if the ATM cell is a point-to-point communication cell, the ATM switching system selects the subscriber ports based on the translated header and transfers the cell of which header is separated to the selected subscriber ports.