A deep understanding of the dissociation and transportation mechanism of natural gas hydrate (NGH), taking into account the effects of geo-stress, contributes to optimizing the development strategy and increases the exploitation efficiency of NGH. In this paper, the mathematical model, coupled with fluid heat and mass transfer, multiphase flow mechanics, and reaction kinetics with phase change in the process of hydrate decomposition was established. An axisymmetric two-dimensional model was developed to simulate the depressurization decomposition process of natural gas hydrate in the Berea sandstones. FLUENT software was used to solve the fundamental governing equations of the multi-phase flow, and UDF programming was employed to program the hydrate decomposition model and the modified permeability model in the dissociation and transportation of NGH. The simulation results were then validated by Masuda’s experimental data. The effects of gas saturation, outlet pressure, temperature, absolute permeability and geo-stress on the decomposition of natural gas hydrate were studied. The results indicated that a higher absolute permeability, higher initial gas saturation, lower outlet pressure, and higher initial temperature advance the decomposition rate of hydrate. Thus, an optimized production plan is essential to promote the extraction efficiency of the NGH. The geo-stress causes a decrease in the porosity and permeability of the porous rock, which restricts the efficiency of the heat and mass transfer by the fluid flow, leading to a slower dissociation and transportation rate of the NGH. Thus, it is important to take geo-stress into consideration and balance the extracting efficiency and the well pressure, especially when the NGH is developed by depressurization.