The generation and regulation of Terahertz (THz) vortex waves are regarded as one of the key technologies for 6G communication, radar detection, and novel sensors. Utilizing artificial metasurfaces to generate vortex waves offers advantages of planarization, integration, and low cost compared to traditional methods. However, conventional design schemes are functionally limited, facing complex parameter design and analysis that require significant time and computational resources. To this end, we propose a THz full-space metasurface device, with switchable operating frequencies, designed based on the phase transition characteristics of vanadium dioxide (VO2) to further enhance the degree of freedom in THz wave control from a spatial dimension. A deep learning-assisted rapid design method for THz vortex wave metasurfaces is introduced, employing a residual neural network (ResNet) and a tandem strategy to quickly obtain meta-atoms meeting phase requirements and achieve integrated array assembly. Using this method, we designed and constructed THz vortex wave metasurfaces with topological charges of 2 and 4. As the trained neural network model requires minimal computation time for predictions with various inputs, it is particularly suitable for designing large-scale metasurfaces composed of units with diverse electromagnetic responses. This work can be well extended to the design of other metasurfaces requiring control of electromagnetic field amplitude and phase.