The cutting machine for cutting logs of web material, includes a cutting head arranged along the feeding path of the logs. The cutting head includes a coupling for a disc-shaped cutting blade and is designed to impart the disc-shaped cutting blade a rotary motion around the axis thereof and a cyclic movement to cut the logs into single rolls, and to allow the logs to move forward along the feeding path. The machine also includes a store unit for disc-shaped cutting blades associated with the cutting head. A handling member is provided to remove a worn disc-shaped cutting blade from the cutting head and replace the worn disc-shaped cutting blade with a new disc-shaped cutting blade taken from the store unit.