The invention discloses a movable foam abrasive jet fire-fighting cutting machine. The cutting machine comprises a fire-fighting cutting tool bit assembly, a high-pressure pipe, an abrasive mixing tank assembly, a supply pipeline, a mixing valve, a liquid A supply assembly, a liquid B supply assembly, a cutting machine power distribution cabinet, a booster pump, an explosion-proof motor, an unloading overflow valve, a safety valve, a pressure gauge, an energy accumulator, a coupling, a filter, a foam liquid assembly base frame, a liquid A pipeline, a liquid B pipeline, a heat exchanger, a pressure equalizer, a heat-sensitive controller, a hot-oil filter, a liquid inlet filter, a heat-sensitive circuit, a circulating pump, a frequency modulation motor, a three-way gate valve, an oil tank and a waterproof electric wire. The liquid A supply assembly and the liquid B supply assembly are used for pumping liquid A and liquid B into the mixing valve to form foam liquid, then the foam liquid is mixed with abrasive in the abrasive mixing tank assembly after passing through the booster pump, foam abrasive jet is formed, and then the foam abrasive jet is accelerated to a supersonic speed through a nozzle of the fire-fighting cutting tool assembly to impact a to-be-cut object, and fire-fighting foam is generated in the cutting process so as to realize fire-fighting cutting.