The magnetic, structural, and vibrational properties of $\mathrm{YM}{\mathrm{n}}_2{\mathrm{O}}_5$ multiferroic have been studied by means of neutron, x-ray powder diffraction, and Raman spectroscopy at pressures up to 6 and $30\mathrm{GPa}$, respectively. Application of high pressure, $P>1\mathrm{GPa}$, leads to a gradual suppression of the commensurate and incommensurate antiferromagnetic (AFM) phases with a propagation vector $q=(1/2,0,q_z\sim 1/4)$ and appearance of the commensurate AFM phase with $q=(1/2,0,1/2)$. This observation is sharply contrasting to general trend towards stabilization of commensurate AFM phase with $q=(1/2,0,1/4)$ found in other $R\mathrm{M}{\mathrm{n}}_2{\mathrm{O}}_5$ compounds upon lattice compression. At $P\sim 16\mathrm{GPa}$ a structural phase transformation accompanied by anomalies in lattice compression and pressure behavior of vibrational modes was observed. The comparative analysis of high-pressure and $R$-cation radius variation effects clarified a role of particular magnetic interactions in the formation of the magnetic states of $R\mathrm{M}{\mathrm{n}}_2{\mathrm{O}}_5$ compounds.