We have investigated optically excited magnetoelastic waves by phase-resolved spin-wave tomography (PSWaT). PSWaT reconstructs the dispersion relation of spin waves together with their phase information by using time-resolved magneto-optical imaging for spin-wave propagation followed by an analysis based on the convolution theorem and a complex Fourier transform. In PSWaT spectra for a Bi-doped garnet film, we found a 180°-phase shift of magnetoelastic waves at around the crossing of the dispersion relations of spin and elastic waves. The result is explained by a coupling between spin waves and elastic waves through the magnetoelastic interaction. We also propose an efficient way for the phase manipulation of magnetoelastic waves by rotating the orientation of magnetization less than 10°.