The invention provides a cutter exploitation method of seabed natural gas hydrates. The method employs a seabed exploitation vehicle, a sea level decomposition and storage system, and a waterpower conveying system for connecting the seabed exploitation vehicle as well as the sea level decomposition and storage system. The seabed exploitation vehicle comprises a reamer, a reamer arm, a crawler type running gear as well as a power and control system, and the like, and is used for cutting and fragmenting the seabed natural gas hydrate. The waterpower conveying system comprises an auxiliary slurry pump, a conveying flexible pipe, a buoyancy ball, a main slurry pump, a conveying hard tube, and the like, and the system is used for conveying the natural gas hydrates which is fragmented by the exploitation vehicle to the sea level decomposition and storage system. The decomposition and storage system comprises a decomposer, a storage container, a mine tailing pipe, and the like, and is used for decomposing and separating the natural gas hydrates which are conveyed by the conveying system and collecting the natural gas hydrates in the storage container, and the separated seabed deposits and other refuses are discharged to the seabed. The cutter exploitation method of seabed natural gas hydrates has high production efficiency and controllable exploitation process, 'air bag' and the like are not needed to construct, and the method has good application prospects.