Overview: In recent years, vortex beams have become the focus of research, and their orbital angular momentum makes them have many important applications, like optical communication, particle manipulation, and optical measurement. At the same time, researchers are paying attention to more abundant generation methods. In previous studies, vortex beam generation methods are usually divided into two categories. The first category is the outcavity, such as spiral phase plate method, spatial light modulator method, mode conversion method, metasurface method, and corner array method, and the second category is the incavity, such as point-loss method, off-axis pumping method, and spatial light modulator method. However, these methods can not tolerate high power laser output and adjust topological charges flexibly. Therefore, how to generate a vortex beam that can tolerate high power laser output and adjust the topological charges flexibly is an important problem to be solved. Continuous surface deformation mirror is a key component of adaptive optical system. In the study of wavefront fitting for continuous surface deformation mirrors, there are usually two kinds of methods. The first type is model-free method, such as genetic algorithm, simulated annealing algorithm, stochastic parallel gradient descent (SPGD) algorithm, etc. These methods generally require many iterations and slow convergence, and it is difficult to change the topological charge flexibly. The second type is pattern method, such as Zernike mode method, Lukosz mode method, and enginmode method. This method first defines a set of complete orthogonal modes, calculates the mode coefficients, and completes the fitting of the target wavefront by linear superposition of each mode. Zernike mode is orthogonal in the circular domain, Lukosz mode is orthogonal in the circular domain derivative. However, usually the configuretion of deformation mirror is not circular domain. For example, the deformation mirror driver used in this paper is arranged in circular domain. In this case, the orthogonal basis needs to be rebuilt to use these two methods. The eigenmode of the deformed mirror is directly and precisely derived from the influence function of the deformed mirror drivers, so it can not only avoid the influence of fitting error, improve the fitting accuracy, but also adapt to the different configuration of the deformed mirror. Combined with the eigenmode method, continuous surface deformation mirror can fit all kinds of vortex beams with high precision and fast fitting speed, and can be applied to all kinds of deformation mirrors with different configurations. In this paper, the eigenmode method of continuous surface deformation mirror is used to simulate and analyze the fitting of the spiral wavefront of integer order with topological charge is ?5 to 5, fractional order, multi-fractional order, and superposition state with the absolute value of topological charge less than 5. Various vortex light fields are generated by dynamic manipulation. The results show that the continuous surface deformation mirror will have a good application prospect in the field of high-power vortex field manipulation.A complete orthogonal basis was constructed by using the eigen-mode method of continuous surface deformation mirror, and the voltage of each driver of the deformation mirror can be obtained according to the spiral wavefront information which needs to be manipulated. The spiral wavefront of integral order, fractional order, multi-fractional order, and superposition state with the absolute value of topological charge less than 5 was generated, and the dynamic manipulation of the vortex beam was realized. The results obtained were the same as those obtained by the ideal spiral wavefront. The ability of the continuous surface deformation mirror to fit the spiral wavefront was demonstrated and good results were obtained. This method has a good application prospect in the dynamic manipulation of high-power vortex laser.