High-power vortex lasers have good application prospects in optical processing and other fields. At present, most methods of generating vortex beams outside the cavity use phase-type devices, such as spiral phase plates and spatial light modulators, and these methods can not withstand high-power laser. The spiral mirrors can be used to generate high-power, but they can not flexibly modulate the vortex beam modes. Thus, the technology of generating mode-tunable high-power vortex beams is still a problem to be solve. In this paper, A method based on the Deformable Mirror (DM) with continuous surface to generate vortex beams is proposed. According to the helical symmetry phase of the vortex beam, the arrangement style of the actuators is designed as a ring, and by generating annular spiral wavefront to solve the DM can not fit singularity. Meanwhile, the annular spiral wavefront has the effect of suppressing side lobes. By comparing the mode purity of the annular spiral wavefront generating via the DM with different numbers drivers, the arrangement of driver arrays is determined, five rings and the number of drives in each ring from the inside to the outside is 15, 20, 25, 30, 35.Since the DM with continuous surface can not produce the ideal spiral wavefront, and the constant size beam used in simulation can not achieve the best effect of sidelobe suppression for the vortex beam with any mode. Therefore, there are high-frequency noise and high-order diffraction sidelobes in the vortex optical field generated by the DM designed. Hence, we add 4f filtering system to the optical path to remove they, and the expression of the radius of the main lobe of the vortex beam on the focal plane is derived as the radius of the filter hole. Finally, The sidelobe-free vortex beams with the topological charge equal to -5~5 are generated by simulation, whose amplitude distribution is a destructive ring, and the phase is quite close to the ideal spiral phase, furthermore, the mode purity is closed to 1 after filtering.The above results prove that the DM with continuous surface combined with the filter system can be used to generate a vortex beam with high mode purity. Moreover, the DM with continuous surface can flexibly generate different wavefront, and can withstand high-power laser, thus, this method has a good application prospect for generating high-power vortex beams with adjustable mode.