The independent control of two orthogonal polarizations that possess dual functionalities is highly desirable in antenna and wireless communication technologies. Spin-decoupled metasurfaces with integrated dynamic and geometric phases have been proposed to generate two independent right-handed and left-handed circularly polarized (RCP and LCP, respectively) waves. However, the RCP and LCP phases are correlated by a linear equation of the dynamic and geometric phases. In this paper, we propose a meta-atom in which the 1-bit phase of two orthogonal polarizations can be controlled independently. Moreover, a high-gain broadband millimeter-wave multidimensional metasurface to generate an x-polarized l = 0 beam with a 10° beam deflection and a y-polarized l = +1 beam independently is simulated, fabricated, and tested. The proposed metasurface operating over the frequency range of 16–28 GHz has the maximum gains of 28.7 dBi and 23.8 dBi for the l = 0 x-polarized waves and l = +1 y-polarized waves, respectively. Compared with spin-decoupled metasurfaces, the proposed metasurface provides a simpler design process to generate two independent vortex beams for the two orthogonal polarizations. The proposed vortex metasurface also has the advantages of dual polarization, high gain, wide relative bandwidth, and is broadband. The proposed metasurface has potential application in high-capacity communication systems.