Field-free switching of perpendicular magnetization via spin-orbit torque (SOT) induced by out-of-plane polarized spin currents is a promising technique for high-density semiconductor and logic devices. However, breaking mirror symmetry for such a switching usually requires complex methods. Herein, we propose that low-symmetry monoclinic materials can break symmetry protection on spin-current polarization and generate unconventional spin currents without additional order parameters or complex structural engineering. Combining symmetry analysis and spin-torque ferromagnetic resonance experiments, we demonstrate that monoclinic WO2 produces out-of-plane polarized spin currents, which is closely related to the crystallographic direction of the applied current. Consistent with the crystalline symmetries, unconventional spin currents along a specific crystallographic direction efficiently drive field-free SOT switching of the perpendicular magnetization at room temperature. Our results demonstrate that low-symmetry materials can serve as efficient spin sources, generating spin currents with specific polarization directions, and may have broad prospects in spintronic applications.