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Inelastic neutron scattering has been used to study the magneto-elastic excitations in the multiferroic manganite hexagonal YMnO₃. An avoided crossing is found between magnon and phonon modes close to the Brillouin zone boundary. Neutron polarization analysis reveals that this mode has mixed magnon-phonon character. An external magnetic field along the c-axis is observed to cause a linear field-induced splitting of one of the spin wave branches. A theoretical description is performed, using a Heisenberg model of localized spins, acoustic phonon modes and a magneto-elastic coupling via the single-ion magnetostriction. The model quantitatively reproduces the dispersion and intensities of all modes in the full Brillouin zone, describes the observed magnon-phonon hybridized modes, and quantifies the magneto-elastic coupling. The combined information, including the field-induced magnon splitting, allows us to exclude several of the earlier proposed models and point to a magnetic ground state, of the P6'₃c'm symmetry, and provides an effective dynamic model relevant for the multiferroic hexagonal manganites.