A media loading and unloading system, for use with a media cutting system having a cutting table and cutting apparatus to cut or score media held on a surface of the cutting table, includes an elevator assembly and a bi-directional transport system. The elevator assembly includes a drive and multiple vertically displaced bins that are vertically movable up and down by the drive. The bi-directional transport system transports media in a lateral feed direction from the elevator assembly to the cutting table surface and removes media from the cutting table surface in a lateral direction opposite to the feed direction to the elevator assembly.