Studies on coral aggregate concrete (CAC) mainly focused on uniaxial stress conditions. However, concrete structures often experience complex stress conditions in practical engineering. The mechanical properties and failure modes are different from those under uniaxial stress. Due to material differences, theories related to ordinary Portland concrete (OPC) cannot be directly applied to CAC. Therefore, it is essential to investigate the mechanical behavior and failure mechanisms of CAC under multiaxial stress conditions. This paper employs a 3D mesoscale model that considers the actual size, shape, and spatial distribution of aggregates. The reliability of the model and material parameters was verified through comparison with existing experimental data. Subsequently, the model was used to systematically study the mechanical properties, failure modes, and failure processes of C40 CAC under different conditions (biaxial compression, biaxial tension-compression, and biaxial tension). The numerical results were compared with the experimental results of CAC and OPC. The results indicate that the failure modes of CAC under biaxial compression are diagonal shear failure, while under biaxial tension- compression and biaxial tension, the failure modes are tensile failure. The biaxial compressive strength and elastic modulus of CAC are greater than those under uniaxial stress and exhibit a significant intermediate principal stress effect. The biaxial compressive strength reaches its maximum value when the stress ratio is 0.5, which is consistent with the conclusions for OPC. The biaxial tension-compression strength and peak strain of CAC decrease with increasing stress ratio. The biaxial tensile strength of CAC is close to its uniaxial tensile strength, with a higher initial elastic modulus and lower peak strain compared to uniaxial conditions. Finally, failure criteria and strength envelopes for CAC under different biaxial stress conditions were established in order to provide a reference for analyzing the strength characteristics and structural design of CAC.