Single-layer slow-release materials have short lifespans due to their rapid initial release behavior. To address this problem, a double-coated persulfate slow-release material was developed in this study. The outer coating layer consists of polycaprolactone–silica sand, which is used to encapsulate an inner layer of polycaprolactone–silica sand and sodium persulfate. Static and dynamic release experiments were conducted to analyze the behavior and degradation capabilities of this material when activated by iron–nitrogen co-doped biochar (Fe@N-BC) for the removal of sulfamethoxazole (SMZ) and ciprofloxacin (CIP) in groundwater. The double-coated material maintains a stable release rate, achieving optimal performance with an outer layer thickness of 0.25 cm and a silica sand to polycaprolactone (PCL) mass ratio between 2 and 5. Optimal degradation rates for SMZ and CIP were observed at a pH of 3. Specifically, 1 mg/L of SMZ was fully degraded within 12 h, while the complete removal of 1 mg/L of CIP occurred within just 2 h. The presence of humic acid and higher initial pollutant concentrations reduced the degradation rates. Among the tested anions, HCO₃⁻ had the most significant inhibitory impact, while Cl⁻ had the least significant impact on degradation performance. Column experiments demonstrated a consistent release of persulfate over a period of 60 days at a flow rate of 0.5 mL/min. Increased flow rates resulted in a shorter lifespan for this slow-release material. The minimum outflows of SMZ and CIP were obtained with a quartz sand mesh size of 40–60 and a flow rate of 0.5 mL/min. These results offer a theoretical basis for the prolonged and stable release of persulfate, as well as the efficient removal of SMZ and CIP from groundwater.