A method for extracting gas by fracturing a coal seam through a combination of hydraulic slotting and multi-stage combustion impact wave comprises cutting slots in an impact borehole using a hydraulic slotting equipment to perform pressure relief and permeability enhancement on a coal seam and enlarge a N2 (nitrogen gas) or CO2 (carbon dioxide gas) storage space, injecting a large amount of N2 or CO2 into the borehole by means of a high pressure gas cylinder and a pressure reducing valve through a gas injection and extraction pipe, then injecting a certain amount of methane and dry air into a high-temperature and high-pressure combustion chamber by means of the high pressure gas cylinder and the pressure reducing valve, so that the gases are mixed and combusted to form high-temperature and high-pressure impact wave to push a piston to compress the N2 or CO2, thereby generating a large number of factures on the coal seam around the impact borehole under guiding action of the slots. The impact wave is repeatedly generated to form a multi-stage impact, and the impact of the next stage is based on the impact of the previous stage, so that the fractures on the coal seam around the borehole are further expanded and run through. After the N2 or CO2 is compressed by means of the multi-stage impact, more fracture networks are formed on the coal seam around the borehole under the guiding action of the slots and the fractures, thereby enhancing the borehole-based efficient gas extraction.