The sealing behavior of fracture-filling minerals in the near-field of the deep geological repository (DGR) is critical for the safe disposal of high-level radioactive waste (HLW). In granite host rocks, natural fractures are often filled with polymineralic assemblages of calcite, quartz, and clay minerals; however, their coupled compaction–pressure solution mechanisms under thermal–hydraulic–mechanical–chemical (THMC) conditions remain poorly understood. In this study, 12 fracture sealing experiments were conducted on Beishan granite and its typical fracture fillings at 90 °C and 15 MPa effective stress, using different pore fluids and systematically varying grain size (75–250 μm), mineral proportions, and clay content. The results demonstrate that pressure solution–precipitation of calcite in saturated CaCO3 solution is the key mechanism for long-term fracture sealing, achieving a compaction strain of 24.6%—substantially higher than those obtained in deionized water (20.6%) and under dry conditions (14.8%). Fine-grained calcite compacts more effectively than its coarse-grained counterpart, reaching a porosity as low as 4.8%; rigid quartz accelerates calcite pressure solution via stress concentration at grain contacts; and a moderate amount of clay minerals (~20 wt%) further reduces porosity to 2.1% through lubrication and micropore filling. The study reveals a multi-stage process transitioning from mechanical compaction to pressure solution–precipitation, and a synergistic sealing mechanism dominated by calcite compaction–pressure solution, augmented by quartz stress transfer and clay lubrication. These findings revise the traditional monomineralic understanding and provide a scientific basis for safety assessment of HLW disposal and the design of natural sealing materials.