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The curve equation of cutter was established which could determine cutting path and mathematical model. The 3-D model of cutter was constructed. Then, the force condition when the cutter working was analyzed. The law of slip shear motion was discussed. The slip shear angle of cutting edge was deduced. The edge curve of cutter was described. With the construction of slip shear motion equation of the nonlinear motion cutter, slip shear angle of the cutter under dynamic conditions was put forward. Finally, the force and movement of cutter were built in 3-D visual simulation. The harvesting robot prototype installed with the designed cutter was performed in cutting experiments, which could snip the diameter of 1～8mm for litchi branch. Results of simulation and physical experiments showed the effectiveness of the slip shear model and movement equation of cutter. Its nonlinear motion could meet the cutting composite trajectory requirements of realizing feed movement and rotary-cutting. Meanwhile, this scheme could reduce the feed motor and transmission mechanism in X- and Y-directions and achieve the function of cutting. The maximum cutting force acquired by simulation and physical cutting tests was 600N. The proposed cutter was suit for the diameter of 1～6mm and had good performance.