Surface acoustic waves (SAWs) traveling on the surface of a piezoelectric crystal can, through the magnetoelastic interaction, excite traveling spin-wave resonance in a magnetic film deposited on the substrate. This spin-wave resonance in the magnetic film creates a time-dynamic surface stress of magnetoelastic origin that acts back on the surface of the piezoelectric and modifies the SAW propagation. Unlike previous analyses that treat the excitation as a magnon-phonon polariton, here the magnetoelastic film is treated as a perturbation modifying boundary conditions on the SAW. We use acoustical perturbation theory to find closed-form expressions for the back-action surface stress and strain fields and the resultant SAW velocity shifts and attenuation. We demonstrate that the shear stress fields associated with this spin-wave back-action also generate effective surface currents on the piezoelectric both in phase and out of phase with the driving SAW potential. Characterization of these surface currents and their applications in determination of the magnetoelastic coupling are discussed. The perturbative calculation is carried out explicitly to first order (a regime corresponding to many experimental situations of current interest) and we provide a sketch of the implications of the theory at higher order.