Industrial robots are emerging for applications in machining critical components such as flange holes for spherical, cylindrical, and other types of vacuum vessel components. However, the main factor limiting their machining applications is the relatively low stiffness of industrial robots, leading to tool path errors during machining. Hence, this paper proposed an integrated error compensation method considering intersecting hole position and axial tolerance constraints. Firstly, a robot machining trajectory is generated, and the cutting allowance and sampling strategy are determined by running the machining trajectory empty run before machining. Then, integrated constraints are introduced, and a new target hole surface is constructed as a mirror surface under the integrated constraints of error compensation. The tool path is adjusted according to the mirror compensation principle to ensure consistency between the machined and nominal holes. The integrated constraints enable a quick and effective assessment of the suitability of the workpiece for precision machining before actual machining, thereby eliminating unnecessary machining of unqualified workpieces and improving productivity. The reconstructed target hole surface satisfies the integrated constraint criterion and achieves a balanced combination of positional and axial tolerances, making full use of both types of tolerances. Finally, the effectiveness of the method is verified on a large workpiece. The experimental results show that the positional error is reduced from uncompensated (1.03, -0.51) mm to compensated (0.25, -0.005) mm, and the axial error of the intersecting hole surface is reduced from uncompensated 22.32 mm to compensated 1.39 mm.