Existing works in the optimization of five-axis machining mainly focus on the efficiency, precision, or dynamic performance of the machine tools, while the performance of other equipment which assists the machining process has not been considered. This paper takes the robot assisted supporting machining of thin-walled blades as the research objective, and proposes an axial-sensitivity-reduction based five-axis toolpath re-scheduling method for facilitating the collaborative support machining with a machine-tool and a robot. The input of the method is lenient, merely including the original toolpath and the workpiece point-cloud model. The output of the method is the re-scheduled toolpath which requires lower motion ability of the assisted support equipment. This is realized by the following approaches. First, an axial sensitivity concept is defined, which quantificationally reflects the influence extent of the machine-tool axis motion on the assisted supporter motion, thus the most sensitive axis which affects the assisted process maximally can be identified. Then, an optimal-partition dual-domain-assisted-fitting method is provided to reconstruct the parameterized geometrical model of blades according to the point-cloud model, thus the multi-value property of the blades which troubles the surface construction is solved. After that, a sensitive-axis-calming bidirectional-tangent-bug-searching method is proposed to re-schedule the toolpath of five-axis machining, thus reducing the sensitivity of the most-sensitive axis. The whole method is universal, because a general cutter model is used and the cutter-contact point keeps invariant after re-scheduling. The correctness and effectiveness of the proposed method are verified by illustration machining tests of a steam turbine blade using an AB-type five-axis machine tool.