Gas hydrates that occur in offshore sediments and onshore permafrost represent a vast source of natural gas. However, current gas production trials indicate that sand production, which refers to the migration of sand into boreholes is an obstacle for long-term safe and efficient gas production from gas hydrate reservoirs. Therefore, understanding sand production behaviors during hydrate mining is especially important. In this study, we conducted laboratory-scale tests to investigate the effect of hydrate saturation and overlying stress on the sand production behaviors of hydrate-bearing sediments with a sand screen before, during, and after hydrate dissociation by depressurization. The synthesized methane hydrate saturations and simulated overlying stresses were ~20%, ~30%, ~40%, ~50%, and ~60% and ~11, ~12, ~13, ~14, and ~15 MPa, respectively. The experimental results indicate that sand production before hydrate dissociation is relatively minor and primarily silty. The amount of sand produced increases and silt, fine sand, and medium sand were observed during and after hydrate dissociation. The mass of sand production increases as hydrate saturation increases under constant overlying stress; however, under constant hydrate saturation, it increases then decreases as overlying stress increases. Friction among particles may become the primary control factor once the overlying stress exceeds a critical value. We considered hydrate saturation and overlying stress to establish a sand production prediction model. Our findings help understand sand production behavior using sand screens during gas production from hydrate reservoirs and provide a reference for sand production control design in future hydrate mining.