Depleted oil and gas reservoirs, owing to their large storage capacity and well-established infrastructure, are attractive sites for storing green energy carriers such as natural gas, hydrogen, and compressed air. During injection–production cycling in underground gas storage (UGS), variations in effective stress can cause repeated stress disturbances in the reservoir and surrounding rock, which may trigger borehole sand production. In this study, laboratory sand-production simulation tests were conducted to evaluate the effects of cyclic-loading stage, upper stress limit, and cycling frequency on borehole damage and sand-production behavior. The results show that sand production is stage-dependent. During the rapid-hardening and stable stages, the borehole remains largely intact and sand production is negligible. Once the failure and collapse stages are reached, borehole integrity deteriorates and sand production increases sharply, with fine particles becoming dominant. Cumulative sand production increases with the upper stress limit. Increasing the upper limit from 80% to 95% leads to a 2.53-fold increase in produced sand mass, together with a higher fine-sand fraction and a shift in the particle-size distribution (PSD) toward smaller sizes. The cycling frequency also plays an important role. When the frequency decreases, cumulative sand production increases and becomes 53.1% higher than the baseline at 0.001 Hz. Meanwhile, the median particle size (D50) decreases, indicating stronger particle breakage under low-frequency cycling. These findings provide guidance for designing injection–production schemes for UGS and for selecting appropriate sand-control completion strategies.