The exploitation of natural gas hydrates (NGHs) reduces the reservoir strength and increases the effective stress, which may trigger stratum settlement and submarine landslides. In particular, commercial-scale production requires the exploitation of NGHs through multiple wells at the same time, which increases the submarine landslide risk. Therefore, it is necessary to study the influences of well layouts on the stability of submarine slopes in the exploitation of NGHs. To this end, a thermo-fluid–solid multifield coupling model that considers the phase change of NGHs in the exploitation process was established. Considering the finite element strength reduction method, an evaluation model was built to analyze the slope stability in the multiwell exploitation of NGHs with the depressurization method. The results show that because NGH decomposition reduces the reservoir strength, the reservoir is compressed overall, and plastic yield zones first occur in the NGH decomposition zone and the slope toe. Finally, a coalesced plastic yield zone propagates throughout the slope. When exploiting NGHs, slope stability is enhanced with increasing well spacing in a multiwell pattern. The linear well layout along the slope dip direction is more conducive to maintaining slope stability than that perpendicular to the slope dip direction. The slope stability decreases with increasing well spacing density but increases with decreasing slope dip. The influence of well layout on submarine slope stability during natural gas hydrate development is studied, which provides a basis for well layouts during gas hydrate exploitation.