A cutting machine having a rotatingly driven cutting tool (2) and a tool guard (1). The tool guard (1) has a first tool guard part (11) which is fixedly mounted with respect to the apparatus and a second tool guard part (12) which can be pivotably mounted relative to the first tool guard part (11). Each tool guard part includes side walls (30, 32) lying adjacent to respective sides of the cutting tool and a center web which connects the two side walls to each other. The center web (31) extends curved in the peripheral direction and is disposed above the cutting tool (2). In order to perform a disturbance-free pendular cut, the pivotable second tool guard part (12) carries a slide piece (40) which projects beyond the end edge (34) of the center web (31) and has a rounded outer slide surface (35) facing away from the center web (31). The end edge (34) faces away from the fixed first tool guard part (11).