Self-collimated propagation and slow-sound effect of spoof acoustic surface waves over a thin solid slab with partially embedded spherical cavities in a square lattice are numerically and experimentally demonstrated. Band structure calculations via the Finite-Element Method reveal that a single spoof surface wave band appears below the air-line, which flattens as the spheres are embedded deeper, leveraging the observation of self-collimated slow spoof modes. For a radius-to-lattice constant ratio of 0.45 and embedding depth of 60% of the radius, the surface band is such that non-diffractive guiding of spoof waves along the  direction can be achieved. Persistent self-collimated propagation of spoof surface waves over long distances is demonstrated through frequency-domain Finite-Element Method simulations. Plane waves incident from air can couple to the self-collimated modes for a wide range of azimuthal angle of incidence up to 60 degrees, where the polar angle of incidence can be in the range of +/- 15 degrees. Self-collimation of spoof waves is experimentally realized by employing a plane-wave source incident from air. In addition, when the embedding depth is higher than 85%, self-collimated slow spoof modes with group indices higher than 15 can be obtained. The observed phenomena can be utilized in two-dimensional acoustic systems such as logic circuits and interferometric sensing devices. Published under license by AIP Publishing.