A control device for a cutting blade, particularly for cutting-off machines for logs of web material, interrupts operation of the cutting blade when deformation of the blade reaches a preset deformation value and resumes operation of the cutting blade when the deformation of the blade is less than another preset deformation value. The control device includes a measuring device for measuring deformation values of at least a portion of the cutting blade, at least one comparator for comparing the measured deformation values with at least one preset deformation value set by an operator, and an actuator which sends, according to signals coming from the comparator, control signals to a motor of the machine to control the start up and/or the stop of the motor.