A cutting machine for cutting a sheet material to be cut, which is put on a cutting table, with a cutting blade provided in a cutting head movable along the cutting table, wherein the cutting blade is used while both sides (11b, 11c) of its cutting edge are ground to keep sharpness of the cutting edge, and the cutting head is provided with: a one side use abrasive whetstone having an abrasive surface to contact and to grind one side of the cutting edge of the cutting blade, an other side use abrasive whetstone having an abrasive surface to contact and to grind the other side of the cutting edge of the cutting blade, and a whetstone holding mechanism that holds abrasive surfaces (12b, 13b), with which the one side use abrasive whetstone and the other side use abrasive whetstone grind the cutting blade, leaving a space between the surfaces and being parallel to states, in which the abrasive surfaces (12b, 13b) of the one side use abrasive whetstone and the other side use abrasive whetstone are sharpened respectively, characterised by a guide shaft, penetrated into the whetstone holding mechanism, for guiding it linearly, and a change over mechanism (17, 18) for moving the whetstone holding mechanism along the guide shaft, and for changing over between a standby state and a one side grinding state or an other side grinding state, in the standby state the abrasive surfaces (12b, 13b) of the one side use abrasive whetstone and the other side use abrasive whetstone being away from both sides of the cutting edge, in the one side grinding state the abrasive surface of the one side use abrasive whetstone being put in contact with the one side of the cutting edge, in the other side grinding state the abrasive surface of the other side use abrasive whetstone being put in contact with the other side of the cutting edge. a one side use abrasive whetstone having an abrasive surface to contact and to grind one side of the cutting edge of the cutting blade, an other side use abrasive whetstone having an abrasive surface to contact and to grind the other side of the cutting edge of the cutting blade, and a whetstone holding mechanism that holds abrasive surfaces (12b, 13b), with which the one side use abrasive whetstone and the other side use abrasive whetstone grind the cutting blade, leaving a space between the surfaces and being parallel to states, in which the abrasive surfaces (12b, 13b) of the one side use abrasive whetstone and the other side use abrasive whetstone are sharpened respectively, characterised by a guide shaft, penetrated into the whetstone holding mechanism, for guiding it linearly, and a change over mechanism (17, 18) for moving the whetstone holding mechanism along the guide shaft, and for changing over between a standby state and a one side grinding state or an other side grinding state, in the standby state the abrasive surfaces (12b, 13b) of the one side use abrasive whetstone and the other side use abrasive whetstone being away from both sides of the cutting edge, in the one side grinding state the abrasive surface of the one side use abrasive whetstone being put in contact with the one side of the cutting edge, in the other side grinding state the abrasive surface of the other side use abrasive whetstone being put in contact with the other side of the cutting edge.