A controller for a cutting machine has a machining power extracting unit for extracting machining power related to machining from the consumed power of the cutting machine, a detection range setter for setting a detection range for the machining power thus extracted, an integrator for integrating output values of the machining power extracting unit within the detection range thus set, a maximum value detector for detecting the maximum value of the output values of the machining power extracting unit within the detection range, and a judging unit for comparing an input signal with a variable comparative reference value and producing a control signal if the input signal exceeds the comparative reference value. The judging unit has an input which is selectively connectable to the machining power extracting unit, the integrator and the maximum value detector.