This work presents a theoretical design and experimental demonstration of a transmissive microwave metasurface for generating dual-vector vortex beams (VVBs). The proposed metasurface consists of an array of pixelated dartboard discretization meta-atoms. By rotating the meta-atoms from 0° to 180°, a Pancharatnam-Barry (P-B) phase covering the full 360° range is achieved, with a transmittance exceeding 90% over the frequency range from 9.7 to 10.2 GHz. The measured results demonstrate that when a linearly polarized microwave normally impinges on the metasurface, the transmitted beams correspond to the dual VVBs with different directions. A good agreement among Poincaré sphere theory, full-wave simulation, and experimental measurement is observed. This proposed transmissive microwave metasurface for VVBs may offer promising applications in communications and radar detection.