The invention relates to a cutting device (101 . . . 106) for a dough extrusion machine (2), comprising a moveable frame (3), a wire (41) or a blade (42) mounted on said frame (3), and a first drive (51, 52) coupled to said frame (3) causing a movement of the frame (3) in a first direction (x). Moreover, the cutting device (101 . . . 106) comprises a second drive (61, 62, 62′) coupled to said frame (3), which causes a movement of the frame (3) in a second direction (z) transverse to the first direction (x). The second drive (61, 62, 62′) can be actuated independently of said first drive (51, 52). In addition, the invention relates to a method of cutting dough by means of said cutting device (101 . . . 106), wherein the first drive (51, 52) and the second drive (61, 62, 62′) are simultaneously actuated during movement of the wire (41)/blade (42).