Electromagnetic waves possessing orbital angular momentum, namely vortex beams, have attracted considerable attention in the fields ranging from optical communications to quantum science, due to their extraordinary information encoding capabilities. Vortex beams are traditionally exhibited with a donut-shaped intensity distribution, where a null intensity center surrounded by a bright ring, caused by the phase singularity. Here we propose and experimentally demonstrate geometric metasurface devices that can generate near-field vortex beams with variable intensity profiles. The generation of a vortex beam with tailored intensity profile is realized by integrating the azimuthal nonlinear phase and spiral phase into the ring-shaped anisotropic air-slit array. As proof-of-principle examples, multiple geometric metasurfaces that generate vortex beams with CN-fold rotational symmetric or asymmetric intensity profile in the near-field are demonstrated in the terahertz domain. This unique capability for terahertz near-field vortex transmutation based on geometric metasurface approach opens an avenue to develop multifunctional integrated systems and system-on-chip devices, holding potential applications in microscopy, integrated photonics, quantum information processing and optical communication.