In a thermal printer, a continuous paper cutting device has an upper and a lower separator located downstream of a platen in the intended direction of paper transport and positioned to face each other with the intermediary of a continuous paper. The upper and lower separators are each provided with an arcuate end in place of a sharp edge for cutting the paper. The paper is formed with notches at opposite ends of each perforation. When a peforation immediately following the printed part of the paper reaches a predetermined position downstream of the arcuate ends of the separators in the direction of paper transport, the paper is brought to a stop. Therefore, the device allows the operator to separate the printed part from the paper along the perforation without resorting to cutters having sharp edges.