Deep-sea hydrate has great commercial exploitation value as a new type of energy, due to huge reserves, wide distribution, cleanliness, and lack of pollution. Accurately, prediction of the mechanical properties of hydrate reservoirs is a key issue for safe and efficient exploitation of deep-sea hydrate. Although there have been some experimental and numerical simulation studies on the borehole stability of the hydrate layer, the influence of temperature and flow on the decomposition of reservoir hydrate is still not well understood. There have been few pure mechanical studies on the stress and strain state of the hydrate formation around the well, and it is impossible to intuitively understand the influence of the wellbore on the original stress state of the hydrate formation. This paper therefore uses a discrete element method to establish a deep-water shallow hydrate reservoir borehole stability model and compares the discrete element numerical model with an elastoplastic analytical model of borehole stability to verify the reliability of the numerical model. A simulation study on the influence of factors such as reservoir depth and hydrate saturation on wellbore stability is carried out. The simulation results effectively present the constitutive characteristics of strain softening of hydrate sediments. According to the different mechanical characteristics, the near-well zone can be divided into a plastic strain softening zone, a plastic strain hardening zone, and an elastic zone. Reservoir depth and hydrate saturation are found to change the stress state near the well. The greater the depth and the lower the hydrate saturation, the greater the borehole shrinkage. The diameter of the optimal horizontal well in the goaf is in the range from 0.6 to 1.2 m.