The invention relates to a cutting machine, in particular for cutting mats to size by means of a blade (21) arranged on a cutting head (8). The cutting head (8) can be displaced by means of a drive in at least two axes. The cutting-to-size of mats requires a vertical cutting angle (B-B) and an inclined cutting angle (C-C) in order to provide the mat cutout with the, in the main, usual bevel cut. In order to adjust the blade (21) from the first cutting angle (B-B) into the second cutting angle (C-C) or vice versa, the cutting head (8) is run up against a stop (17) arranged on the cutting machine and is brought into contact in such a way that a swivellable element (20) carrying the blade (21) is swivelled from one into the other cutting angle (B-B, C-C). This adjustment can thus take place in an automatically controlled manner, without an additional drive being required for this.