A spark erosion machine includes a frame with a space for spark erosion of a workpiece, a wire for cutting by spark erosion, and a wire guide head for guiding the wire across the workpiece, so as to detach an offcut from it; an offcut support mounted movably relative to the guide head, the support being configured to move at least between a retention position under the spark erosion space, where it can collect the offcut, and a retracted position; and an offcut extractor.