A method for cutting logs of wound web material, comprising the steps of: providing a feeding path for the logs to be cut; arranging along the feeding path a cutting head with at least one disc-shaped cutting blade, the cutting head moving the disc-shaped cutting blade with a cyclical motion to cut the logs and allow a forward movement of the rolls along the feeding path; providing at least one storage unit for disc-shaped cutting blades (9: 9A-9E) associated with the cutting head; wherein the storage unit comprises a blade-holder provided with a plurality of seats for the disc-shaped cutting blades (9; 9A-9E), arranged and configured to keep the disc-shaped cutting blades (9: 9A-9E) coaxial with one another; moving logs of web material sequentially along the feeding path in a direction parallel to the log axis; cutting the logs by means of the disc-shaped cutting blade mounted on the cutting head and severing the logs into small rolls having an axial length smaller than the logs; periodically grinding the disc-shaped cutting blade by means of a pair of grinding wheels associated with the cutting head, the grinding wheels being arranged and controlled to periodically grind the disc-shaped cutting blade mounted on the cutting head; when the disc-shaped cutting blade has so worn that must be replaced: temporarily stopping the forward movement of the logs; removing the worn disc-shaped cutting blade from the cutting head; taking a new disc-shaped cutting blade (9; 9A-9E) from the storage unit, transferring the new disc-shaped cutting blade to the cutting head and mounting it on the cutting head; once the new disc-shaped cutting blade (9; 9A-9E) has been mounted on the cutting head, re-start the forward movement of the logs along the feeding path. providing a feeding path for the logs to be cut; arranging along the feeding path a cutting head with at least one disc-shaped cutting blade, the cutting head moving the disc-shaped cutting blade with a cyclical motion to cut the logs and allow a forward movement of the rolls along the feeding path; providing at least one storage unit for disc-shaped cutting blades (9: 9A-9E) associated with the cutting head; wherein the storage unit comprises a blade-holder provided with a plurality of seats for the disc-shaped cutting blades (9; 9A-9E), arranged and configured to keep the disc-shaped cutting blades (9: 9A-9E) coaxial with one another; moving logs of web material sequentially along the feeding path in a direction parallel to the log axis; cutting the logs by means of the disc-shaped cutting blade mounted on the cutting head and severing the logs into small rolls having an axial length smaller than the logs; periodically grinding the disc-shaped cutting blade by means of a pair of grinding wheels associated with the cutting head, the grinding wheels being arranged and controlled to periodically grind the disc-shaped cutting blade mounted on the cutting head; when the disc-shaped cutting blade has so worn that must be replaced: temporarily stopping the forward movement of the logs; removing the worn disc-shaped cutting blade from the cutting head; taking a new disc-shaped cutting blade (9; 9A-9E) from the storage unit, transferring the new disc-shaped cutting blade to the cutting head and mounting it on the cutting head; once the new disc-shaped cutting blade (9; 9A-9E) has been mounted on the cutting head, re-start the forward movement of the logs along the feeding path.