The invention relates to a mud drying system and a use method thereof. The mud drying system comprises a transcritical heat pump auxiliary heat supplying loop, a heat pump auxiliary heat supplying loop, an air heating and waste heat recovering loop and a hot water circulation loop; the transcritical heat pump auxiliary heat supplying loop comprises an evaporator, an internal heat exchanger, a compressor, a gas cooler and a throttle valve; the heat pump auxiliary heat supplying loop comprises an evaporator, a wastewater and waste heat recovering evaporator, an internal heat exchanger, a compressor, a condenser, a throttle valve, two stop valves and a wastewater tank; the air heating and waste heat recovering loop comprises a hothouse, an air compressor, a gas discharging and carrying port, a first evaporator, the other evaporator and a condenser; and the hot water circulation loop comprises a pump, a hothouse and the condenser in the heat pump auxiliary heat supplying loop. The invention adopts the hothouses to obtain solar energy to heat mud and utilizes the transcritical heat pump auxiliary heat supplying loop and the heat pump auxiliary heat supplying loop to recover the sensible heat and the latent heat in humid air to heat mud, thereby lowering the energy consumption for drying the mud. The invention can be widely applied to various mud processing fields.