A saw machine for cutting logs of web material, comprising: a feeding path for the logs to be cut; a cutting head arranged along the feeding path; a disc-shaped cutting blade, which is mounted on the cutting head, rotates around a rotation axis (B-B) and is provided with a cyclic movement for cutting the logs; two grinding wheels (32, 34), which are arranged and configured to grind two sides of a cutting edge of the disc-shaped cutting blade, and each of which rotates around its own rotation axis (C-C; D-D); wherein the grinding wheels (32, 34) are supported idle and driven into rotation by friction with the disc-shaped cutting blade; characterized in that the grinding wheels (32, 34) are arranged with respect to the disc-shaped cutting blade such that, in a contact area (Z32, Z34) between each grinding wheel (32; 34) and the disc-shaped cutting blade, the grinding wheel (32; 34) has a velocity directed towards the inside of the cutting edge; the grinding wheels (32, 34) are arranged with respect to the disc-shaped cutting blade such that the contact areas (Z32, Z34) between the grinding wheels (32, 34) and the disc-shaped cutting blade are arranged between two planes (P32; P34), each of which contains the rotation axis (C-C, D-D) of a respective one of the grinding wheels (32; 34); said planes are approximately parallel to each other and to a further plane containing the rotation axis (B-B) of the disc-shaped cutting blade, said plane containing the rotation axis (B-B) of the disc-shaped cutting blade being arranged between the two planes (P32, P34) containing the rotation axes (C-C; D-D) of the grinding wheels (32, 34). a feeding path for the logs to be cut; a cutting head arranged along the feeding path; a disc-shaped cutting blade, which is mounted on the cutting head, rotates around a rotation axis (B-B) and is provided with a cyclic movement for cutting the logs; two grinding wheels (32, 34), which are arranged and configured to grind two sides of a cutting edge of the disc-shaped cutting blade, and each of which rotates around its own rotation axis (C-C; D-D); wherein the grinding wheels (32, 34) are supported idle and driven into rotation by friction with the disc-shaped cutting blade; characterized in that the grinding wheels (32, 34) are arranged with respect to the disc-shaped cutting blade such that, in a contact area (Z32, Z34) between each grinding wheel (32; 34) and the disc-shaped cutting blade, the grinding wheel (32; 34) has a velocity directed towards the inside of the cutting edge; the grinding wheels (32, 34) are arranged with respect to the disc-shaped cutting blade such that the contact areas (Z32, Z34) between the grinding wheels (32, 34) and the disc-shaped cutting blade are arranged between two planes (P32; P34), each of which contains the rotation axis (C-C, D-D) of a respective one of the grinding wheels (32; 34); said planes are approximately parallel to each other and to a further plane containing the rotation axis (B-B) of the disc-shaped cutting blade, said plane containing the rotation axis (B-B) of the disc-shaped cutting blade being arranged between the two planes (P32, P34) containing the rotation axes (C-C; D-D) of the grinding wheels (32, 34).