<p>We develop an effective spin-spin coupling framework to describe magnon-phonon hybridization in magnetoelastic systems, where both quasiparticles carry intrinsic spin angular momentum. The strength of the magnon-polaron anticrossing is shown to depend explicitly on the relative orientation of magnon and phonon spins, providing a unified framework for understanding chiral coupling. To validate this theory, we introduce a self-consistent frequency-domain micromagnetic simulation method incorporating full magnetoelastic coupling, which efficiently captures the dispersion and excitation dynamics of hybrid modes with excellent agreement between numerical and analytical results. Based on the polarization-selective magnon excitation governed by magnon-phonon spin alignment, we propose a scheme for acoustic-assisted probing of magnetic domains by exploiting polarization-controlled elastic waves. This work offers a new perspective for spin mechanics, where the spin degrees of freedom of both phonons and magnons are treated on equal footing, revealing their joint role in mediating coherent magnetoelastic couplings.</p>