The cyclic methane hydrate production method was proposed with CO2 and N2 mixture stimulation. The cyclic production model was established based on actual hydrate reservoir parameters, accordingly, the production characteristics were analyzed, and a sensitivity analysis was conducted. The results show the following: (1) The depressurization mechanism is dominant in the cyclic production. CH4 production and CH4 hydrate dissociation can be greatly enhanced because the cyclic process can effectively reduce the partial pressure of CH4 (gas phase). However, there is a limited effect for CO2 storage. (2) Heat supply is essential for continuous hydrate dissociation. The CH4 hydrate dissociation degree is the highest in the near-wellbore area; in addition, the fluid porosity and effective permeability are significantly improved, and the reservoir temperature is obviously decreased. (3) The initial CH4 hydrate saturation, absolute permeability, intrinsic CO2 hydrate formation kinetic constant, injection time and production time can significantly influence the production performance of the natural gas hydrate reservoir.