Heat exchangers (HXs) based on triply periodic minimal surface (TPMS) architectures have recently attracted significant interest due to their continuous and smooth shell structures with extensive surface areas. This study proposes an efficient design methodology for TPMS-based HXs by employing three gradation strategies to enhance their thermofluidic performance: (i) filtering gradation to guide hot and cold fluids through designated inlet and outlet regions with reduced flow resistance; (ii) cell-size gradation to ensure uniform flow distribution by reducing dead zones; and (iii) level-set gradation to maintain a minimum allowable wall thickness under cell-size variations. These multifunctional gradations are realized through adaptive manipulation of the signed distance fields for TPMS formulations. Computational fluid dynamics simulations were performed for various HX designs, identifying a graded design with cell sizes ranging from 6 to 10 mm as optimal for minimizing local flow stagnation. The optimized HX was fabricated via additive manufacturing and validated experimentally. Experimental results revealed a 30% improvement in heat exchange capacity with only a 0.3 kPa increase in pressure drop, resulting in a 28% enhancement in the overall heat exchange performance. These findings demonstrate that the multifunctional gradation approach enables the optimal design of TPMS-based HXs with superior thermofluidic performance and structural integrity.