Recently, the iron containing langasite-type crystal Ba3NbFe3Si2O14 has attracted great attention as a new magnetically induced multiferroic. In this work, magnetic, structural and electronic properties of the multiferroic Ba3NbFe3Si2O14 were investigated by several methods, including synchrotron X-ray diffraction, Raman spectroscopy and synchrotron Mössbauer source technique at high quasi-hydrostatic pressures (up to 70 GPa), created in diamond anvil cells. At room temperature, two structural transitions at pressures of about 3.0 and 17.5 GPa were detected. Mössbauer studies at high pressures revealed a radical change in the magnetic properties during structural transitions. At pressures above 18 GPa, the crystal transforms into two magnetic fractions, and in one of them the Néel temperature (TN) increases by about four times compared with the TN value in the initial phase (from 27 to 115 K). At pressures above 50 GPa, a spin crossover occurs when the fraction of iron Fe3+ ions in oxygen octahedra transits from the high-spin (HS, S = 5/2) to the low-spin (LS, S = 1/2) state. This leads to a new change in the magnetic properties. The magnetic ordering temperature of the LS sublattice was found to be of about 22(1) K, and magnetic correlations between HS and LS sublattices were studied.