There is extensive research on the mechanical behavior of triply periodic minimal surface (TPMS)-based lattices, but no experimental studies have specifically examined the impact response of sandwich structures incorporating additively manufactured stainless steel 316L TPMS-lattice cores with woven carbon fiber-reinforced polymer skins. This study investigates the low-energy (120 and 130 J) drop-weight impact behavior of such sandwich composites, focusing on the influence of TPMS-lattice core topology (gyroid, diamond, primitive, and IWP), relative density (8–20%), and cell size (5 and 10 mm) on both single-hit and multi-hit impact resistance. Micro-computed tomography was employed to assess internal damage and deformation patterns within the impact zone. The results reveal that higher core densities and larger cell sizes enhance impact resistance and improve composite skin protection. Under the single-impact conditions, the gyroid lattice exhibited a better impact resistance, followed by diamond, primitive, and IWP. However, under multi-hit conditions, the diamond-based sandwich composite outperformed the gyroid due to the increased lattice densification within the impact zone, in addition to its superior combined uniaxial and shear resistance. In summary, a precise control over the topological features of sheet-based TPMS-lattice cores enables a more informed decision-making when designing sandwich composites for specific engineering applications, particularly in dynamic loading scenarios.