The structural, magnetic and electronic properties of Mn2YSn (Y=Sc, Ti, and V) Heusler alloys under applied hydrostatic pressure are studied by the first-principle calculations and Monte Carlo simulations. We find that two magnetic reference states with low and high magnetic moment at the low and high crystal lattice volume, respectively, can coexist together due to the almost equal energy under applied pressure of 3.4, −2.9 and −3.25 GPa for Mn2ScSn, Mn2TiSn, and Mn2VSn, correspondingly. The positive/negative pressure correspond to the uniform lattice contraction/expansion. We show that for all compounds, the low magnetic state (LMS) is characterized by the almost half-metallic behavior and it is maintained against hydrostatic pressure. However, the electronic structure of the high magnetic state (HMS) takes on a metallic character. For HMS, the magnetic exchange parameters and Curie temperatures are found to be sufficiently larger values as compared to those of LMS. To identify stable phases at given pressures, the phase diagrams are constructed. The pressure-induced switching mechanism between almost half-metallic and metallic states with different magnetization is proposed.