The invention discloses a marine gas hydrate and mortar replacement exploitation method and device. According to the exploitation method, the sand blocking accuracy of a mechanical screen pipe is properly lowered to enable stratum mud and sand fine particles to flow into a shaft production pipe column and be discharged under the controllable condition, in the meantime, coarse-particle mortar is injected into a hydrate reservoir continuously, and through matching of a hydrate reservoir sand outlet management technology and mortar injection technology, replacement of the coarse-particle mortar and the stratum fine particles as well as the coarse-particle mortar and a hydrate space is achieved. The exploitation device comprises a production sleeve pipe, a production oil pipe, a shaft water injection pipe and a mortar back-injection pipe, the lower end of the production sleeve pipe is connected with the mechanical screen pipe, and the upper end and the lower end in the mechanical screen pipe are further provided with an upper mechanical packer and a lower mechanical packer correspondingly. The inlet end of the production oil pipe is provided with a gas separating device, and the position, above the upper mechanical packer, of the shaft water injection pipe communicates with the production oil pipe. The mortar back-injection pipe penetrates through the upper mechanical packer and the lower mechanical packer, extends to the bottom border of the production layer section of the hydrate reservoir and is connected with a gravel filling tool. Through the method and the device, the purpose of continuous and efficient production is achieved.