We have performed an ab initio study of disordered ferrimagnetic Ni_1.9375Mn_1.5625Sn_0.5 martensite. Employing the supercell approach combined with the special quasi-random structure concept for modeling of disordered states we have determined thermodynamic, magnetic, structural, elastic and vibrational properties of the studied material. Its atomic and magnetic configuration is found to exhibit a pressure-induced increase of the total magnetic moment, i.e. the total magnetic moment increases with decreasing volume. This peculiar trend is revealed despite of the fact that the magnitudes of local magnetic moments of atoms decrease (or stay constant) with decreasing volume. The origin of the identified phenomena may be related to (i) the ferrimagnetic nature of the magnetic state when the parallel and antiparallel magnetic moments nearly compensate each other and (ii) chemical disorder that leads to different local atomic environments and, consequently, also to different local magnetic moments and their different response to hydrostatic pressures (the antiparallel moments are more sensitive). The studied state is mechanically and dynamically stable (no imaginary-frequency phonons) but, regarding its thermodynamic stability, it is an excited state.