Owing to the increasing application of cementitious grout in strengthening projects in cold regions, the freeze–thaw durability of the bond between cementitious grout and concrete has attracted attention. This study investigates the bond performance of a cementitious grout–normal concrete interface after FTCs through splitting tensile and slant shear tests at different angles. The microstructure of the cementitious grout–concrete interface is observed via backscattered electron (BSE) microscopy. The results show that FTCs rapidly reduce the splitting bond strength and slant shear bond strength of the interface. After 240 FTCs, the splitting and slant shear bond strengths decrease by 40.7%–72.4% and 46.1%–57.3%, respectively. An increase in substrate strength significantly enhances the interfacial bond strength, particularly the slant shear bond strength. Freeze–thaw damage to the substrate reduces the interfacial bond strength and frost resistance. The slant shear strength increases significantly with the slant shear angle. The effects of FTCs on the interfacial shear strength parameters are reflected through a rapid decrease in cohesion, whereas the interface internal friction angle remains relatively unaffected. Empirical formulas for calculating the interface bond strength are obtained from experimental data and validated. The BSE images show that cracks begin to appear at the cementitious grout–normal concrete interface as the number of FTCs increases, thereby decreasing the interfacial bond strength.