Currently, vortex beams are extensively utilized in the information transmission and storage of communication systems due to their additional degree of freedom. However, traditional terahertz metasurfaces only focus on the generation of narrowband vortex beams in reflection or transmission mode, which is unbeneficial for practical applications. Here, we propose and design terahertz metasurface unit cells composed of anisotropic Z-shaped metal structures, two dielectric layers, and a VO2 film layer. By utilizing the Pancharatnam–Berry phase theory, independent control of a full 2π phase over a wide frequency range can be achieved by rotating the unit cell. Moreover, the full-space mode (transmission and reflection) can also be implemented by utilizing the phase transition of VO2 film. Based on the convolution operation, three different terahertz metasurfaces are created to generate vortex beams with different wavefronts in full-space, such as deflected vortex beams, focused vortex beams, and non-diffraction vortex beams. Additionally, the divergences of these vortex beams are also analyzed. Therefore, our designed metasurfaces are capable of efficiently shaping the wavefronts of broadband vortex beams in full-space, making them promising applications for long-distance transmission, high integration, and large capacity in 6G terahertz communications.