To easily carry out a cut piece by preventing the cut piece from being drawn in the cutting direction by a cutting tool when the cutting is completed even when the cut piece is extremely small.

A speed changing means 71 is controlled to change the downward moving speed of a cutting head 31 from a quick-feed speed to a cutting feed speed when a filter 79 is brought into contact with a work W and moved in a relatively upward direction with respect to the cutting head 31, a pressing unit 87 to press a cut piece portion WA in the work W against a lower end of the tiller 79 from an upper direction is provided, and an urging means 91 to urge the filler 79 against the head 31 is provided.