This paper designs and fabricates small-angle grid sandwich composites and carbon fiber composite panels by adjusting core support angles, integrating the advantages of two-dimensional (2D) periodic and three-dimensional (3D) lattice sandwich structures. The effects of core angle and height on the bending and flatwise compression performance of the composites are investigated, and finite element simulations are conducted via ABAQUS to verify experimental results and comprehensively analyze failure mechanisms. The results show that the small-angle grid sandwich structures exhibit better anti-deformation performance than 2D periodic sandwich structures and are easier to form than 3D lattice sandwich structures. The bending properties of composites with small-angle grid core are superior to those with 90° 2D periodic cores, and core shear failure is the dominant failure mode. At the same core height, reducing the angle between grid support sheets and skins increases the bending failure load; compared with α = 90°, α = 60° increases the load by 33.2–71.9% at H = 6–10 mm. At the same core angle, increasing core height gradually raises the bending failure load; H = 10 mm shows 72–97% higher load than H = 6 mm at α = 60–90°. For flat compression, failure is mainly caused by core wrinkling and collapse. Core angle has little effect on the compressive load at H = 6–8 mm, while the compressive failure load decreases with increasing core angle at H = 9–10 mm.