A machine for cutting a moving object comprises a conveyor belt for carrying the object along an advancement direction at a line speed and comprises a driving and cutting unit configured to move in a cutting cycle according to a forward phase in order to perform the cutting of the moving object, and configured to move according to a return phase in order to return into the initial position of the cutting cycle. The cutting machine further comprises a processing unit configured to generate a driving signal for controlling the movement of the driving and cutting unit with an acceleration trend wherein the maximum absolute value of the acceleration within the return phase is smaller than the maximum absolute value of the acceleration within the forward phase.