Disclosed is a line catcher-type waterjet cutting apparatus in which a workpiece is subjected to the waterjet processing in a state of being clamped by a workpiece edge clamping device and a separate driving unit for the workpiece edge clamping device is provided, and in which the workpiece is clamped by the workpiece edge clamping device during the waterjet processing, while the workpiece is easily decoupled from the workpiece edge clamping device after the waterjet processing is completed, so that the waterjet processing is carried out while reciprocally conveying the workpiece in an X-direction, thereby increasing the processing accuracy of the waterjet processing and easily automating the waterjet processing.