The invention discloses a workpiece-movable metal cutting machine and belongs to the field of metal cutting technologies. In order to generate new starting points continuously in the process of metal cutting of a grinding wheel of the metal cutting machine, reduce the contact area of the cylindrical surface of the grinding wheel and a workpiece in the cutting process and more effectively cut metal, the invention adopts the following technical measures that flat tongs are movably mounted on a working table of the metal cutting machine, and the flat tongs can drive the workpiece to move in the direction perpendicular to the middle line of a grinding wheel rotary shaft and feed direction when the metal cutting machine cuts metal, so that the circumference of the grinding wheel does not coincide with an original cutting trace any more after the workpiece moves, and the new cutting starting points are generated. The flat tongs on the workpiece-movable metal cutting machine are movably mounted on the working table so that when the workpiece-movable metal cutting machine cuts the metal, the new starting points can be generated continuously and the friction area between the cylindrical surface of the grinding wheel and the metal can be reduced, and accordingly, operation is easy when the metal workpiece with a large end face area is cut.