Triply periodic minimal surface (TPMS) cellular structures are widely recognized for their exceptional lightweight properties and energy absorption capabilities. Achieving optimal crashworthiness necessitates a thorough understanding of design parameters and a comparative analysis of TPMS forms. This study investigates the influence of design parameters, specifically the level set constant and unit cell length, on the crashworthiness of TPMS cellular structures. The deformation behavior and crash performance of TPMS structures are examined by utilizing nonlinear finite element analysis via LS-DYNA. A comparative analysis between two prominent TPMS forms, Isotropic Woodpile (IWP) and Förstner Random Dots (FRD), is conducted. The results underscore the substantial impact of design parameters on the crashworthiness of TPMS cellular structures. FRD demonstrates superior crashworthiness characteristics, including enhanced specific energy absorption and reduced initial peak force, particularly at low relative density, surpassing the performance of IWP. These findings highlight the potential of TPMS structures, especially FRD, as promising candidates for energy absorber design, given their lightweight nature and exceptional crashworthiness properties. The study's comprehensive investigation of design parameters and comparative analysis enhances the understanding of TPMS cellular structures, offering valuable insights for optimizing their crashworthiness in energy absorption applications.