The utilization of red mud in the production of ceramic products represents an efficient approach for harnessing red mud resources. Composite ceramics were prepared from Al2O3, red mud, and Cr2O3 by atmospheric pressure sintering, and the phase composition and microscopic morphology of the composite ceramics were investigated by XRD, SEM, and EDS. The flexural strength and fracture toughness of composite ceramics were measured by three-point bending and SENB methods. The results showed that the composite ceramics sintered at 1500 °C with the addition of 1.5 wt.% Cr2O3 had a flexural strength of 297.03 MPa, a hardness of 17.44 GPa, and a densification of 97.75% and fracture toughness of 6.57 MPa·m1/2. The addition of Cr2O3 helps to improve the low strength of red mud composite ceramic samples. The CaAl12O19 phase can form a similar “endo-crystalline” structure with Al2O3 grains, which changes the fracture mode of the ceramics and thus significantly improves the fracture toughness. The wettability tests conducted on Cu and RM–Al2O3 composite ceramic materials revealed that the composites exhibited non-wetting behavior towards Cu at elevated temperatures, while no interfacial reactions or elemental diffusion were observed. Composites have higher surface energy than Al2O3 ceramic at high temperatures. The present study provides a crucial foundation for enhancing the comprehensive utilization value of red mud and the application of red mud ceramics in the field of electronic packaging.