Hyperbolic metasurfaces have recently emerged as a new research frontier because of the unprecedented capabilities to manipulate surface plasmon polaritons (SPPs) and many potential applications. However, thus far, the existence of hyperbolic metasurfaces has neither been observed nor predicted at low frequencies because noble metals cannot support SPPs at longer wavelengths. Here, we propose and experimentally demonstrate spoof plasmonic metasurfaces with a hyperbolic dispersion, where the spoof SPPs propagate on complementary H-shaped, perfectly conducting surfaces at low frequencies. Thus, non-divergent diffractions, negative refraction and dispersion-dependent spin-momentum locking are observed as the spoof SPPs travel over the hyperbolic spoof plasmonic metasurfaces (HSPMs). The HSPMs provide fundamental new platforms to explore the propagation and spin of spoof SPPs. They show great capabilities for designing advanced surface wave devices such as spatial multiplexers, focusing and imaging devices, planar hyperlenses, and dispersion-dependent directional couplers, at both microwave and terahertz frequencies.