The cutting machine includes at least one feed path for elongated products, wherein the elongated products move forward along a direction substantially parallel to the longitudinal extension thereof. The cutting machine includes a rotating unit adapted to rotate around a rotation axis, carrying at least one first disc-shaped cutting blade and one second disc-shaped cutting blade. The rotation of the rotating unit causes an orbital movement of the first disc-shaped cutting blade and of the second disc-shaped cutting blade along trajectories intersecting the product feed path. The first disc-shaped cutting blade and the second disc-shaped cutting blade are offset from each other in a direction parallel to the product feed path. The first disc-shaped cutting blade and the second disc-shaped cutting blade are also angularly offset from each other with respect to the rotation axis of the rotating unit.