Sandwich composite structures are comprised of a low-density core (commonly honeycomb) and facesheets. They are typically used in applications that require lightweight for efficient design, such as in the marine and aerospace industries. This work investigates the feasibility of adopting triply periodic minimal surface (TPMS) cellular structures as the core for sandwich composites. Sandwich structures were manufactured using a carbon fiber-reinforced polymer (CFRP) facesheet and three different 304 L stainless steel core structures (honeycomb, gyroid TPMS, and diamond TPMS). Three mechanical tests, namely edgewise compression, three-point bend, and impact test, were carried out to evaluate the performance of each sandwich configuration. The experimental results of the non-traditional sandwich configurations were compared against those of a honeycomb core sandwich composite. The edgewise compression test showed that the ultimate edgewise compressive strength increased by 7% when the honeycomb core was replaced by the gyroid core and reduced by 2% when the diamond core replaced the honeycomb core. The three-point bend test showed that the traditional honeycomb core sandwich configuration had a higher shear yield stress when compared to the non-traditional sandwich structures. The shear yield stress was reduced by 54% when non-traditional sandwich cores were used. The shear ultimate stress was reduced by 41% and 37% when the honeycomb core was replaced by the gyroid and diamond structure, respectively. Impact test results, on the other hand, showed that the peak force recorded during the impact event was reduced, while the absorbed energy was increased when non-traditional cores were used. Peak force was reduced by 28% and 39%, while the absorbed energy was increased by 9% and 16% when the honeycomb core was replaced by the gyroid and diamond cores, respectively.