Composite sandwich panels, due to their unique mechanical properties such as high strength-to-weight ratio, possess significant potential for use in lightweight aerospace structures. In this study, the effect of core structure and thickness variation on the structural performance of these panels is investigated. The structure consists of a polyamide core with honeycomb, re-entrant auxetic, and sinusoidal auxetic patterns, and composite face sheets made of glass fibers and polyamide resin. Three-point bending tests were conducted to examine the influence of core thickness on flexural strength, load-bearing capacity, and displacement prior to failure. The results indicate that increasing the core thickness directly enhances the load-bearing capacity and flexural strength of the structure. Among the configurations studied, the beam with a sinusoidal auxetic core exhibited the highest load-bearing capacity, such that increasing the thickness from 1.5 mm to 2.5 mm led to a 36% rise in the maximum load endured. In contrast, the honeycomb structure showed the highest elastic displacement, indicating greater flexibility of this core. Furthermore, the increase in thickness in the re-entrant auxetic structure had the most significant effect on improving flexural strength, although the load-bearing enhancement was lower compared to the other two configurations. A comparison of load-to-mass and absorbed energy indices revealed that both core geometry and cell wall thickness have substantial effects on the mechanical performance of sandwich structures. Scanning electron microscope (SEM) images also revealed brittle fracture in the cores.