The spiral cutter is the most important working part of the bowl jellyfish automatic cutting machine. In order to ensure the stability of the work, the elastic deformation and the good service life are avoided. The mathematical model of the cutter blade line is established by using the differential geometry. The curvature and torsional size and the law of curvature and torsion with polar angle are simulated by MATLAB. The maximum value of the curvature is 1.57, the minimum is 0.012 47, the maximum torsion is 0.002 46, and the minimum is 0. The three - dimensional solid model of spiral cutter was established by using Solidworks software, and it was introduced into ANSYS Workbench to complete the static analysis. The stress, strain and maximum deformation position of spiral cutter structure were determined, and the structure design of spiral cutter was proved to meet the performance requirement. The research results can provide a basis for studying the fatigue damage, service life and optimization of the bowl-shaped jellyfish screw cutter.