It is an object of the present invention to provide a cutting machine capable of keeping an angle of a cutting edge constant. A support block 14 is provided with two arms 14a, 14b which are spaced at a certain angle, and the arms 14a, 14b have rotation shafts 12a, 13a of rotary whetstones 12, 13, respectively, extending upright from the vicinities of the front ends thereof. The rotary whetstones 12, 13 has, at front ends thereof, flat surfaces 12b, 13b perpendicular to the rotation shafts 12a, 13a to grind the one side 11b and the other side 11c of the cutting edge 11a of the cutting blade 11, respectively. The whetstone holding mechanism 15 can be moved linearly along the guide shaft 16 and can change over grinding states in which the flat surfaces 12b, 13b of the rotary whetstones 12, 13 into contact with the one side 11b or the other side 11c of the cutting blade 11. Even when the grinding progresses, since parallelism between the flat surfaces 12b, 13b and the one side 11b and the other side 11c of the cutting blade 11, so that the angle of the cutting edge is kept constant.