To explore the influence of different stress states and angles of inclination of bonding surface on the mechanical properties of caesious sandstone-mortar composites during tunnel construction, triaxial compression tests on caesious sandstone-mortar composites under different angles of inclination and confining pressures were carried out. The evolution patterns of the strength, deformation characteristics, and damage modes of these composites were analyzed. Based on the crack closure effect, anaxial crack closure model of the composites was developed, and its rationality was verified. The results show that as the confining pressure increases, the yielding behavior of the caesious sandstone-mortar composites becomes less obvious. In addition, the confining pressure has the greatest effect on improving the strength of the composite with an angle of inclination of 60°. The peak strain and elastic modulus are positively correlated with the confining pressure. As the angle of inclination increases, the peak strength and cohesion change in an “N”-shaped manner. The composite with an angle of inclination of 60° has the lowest peak strength. Under high confining pressure, the composite with an angle of inclination of 60° experiences overall slip instability along the contact surface, but other composites with different angles of inclination undergo shear damage penetrated with a single main crack. The established axial crack closure model of the composites can effectively describe the relationship between the pre-peak axial stress and strain curves.