A system automatically weeds around graphics cut into a sheet of sign material having a backing and utilizes a tool moved relative to the sign material sheet along a path offset from the lines of cut defining the graphic in response to commands issued by a controller to selectively bond an overlay sheet to the weed portions of the sign material sheet. The overlay sheet is placed over the sign material sheet and is selectively bonded with portions of the cut sign material sheet for subsequent separation of the nongraphic or weed material from the cut graphic when the overlay sheet is pulled away from the backing.