The dissipation of ion-acoustic surface waves in a fully ionized and semi-bounded plasma is investigated by solving the dispersion integral formulated by employing the specular reflection boundary condition. Non-zero ion temperature and ion-ion collisions are considered in the dielectric permittivity. The calculated damping rate is composed of the collisionless Landau damping and the collisional dissipation. The distinctions between them are addressed here. It is found that the collisionless damping is significant in the region where the wavelength is larger than the electron Debye length. The collisional dynamics, however, as well as the ion temperature, dominates the wave damping when the wavelength is smaller than the electron Debye length.