We report on abrupt changes in dc resistance and impedance of a diode with the Schottky barrier based on the Mn/SiO2/p-Si structure in a magnetic field. It was observed that at low temperatures the dc and ac resistances of the device change by a factor of more than 106 with an increase in a magnetic field to 200 mT. The strong effect of the magnetic field is observed only above the threshold forward bias across the diode. The ratios between ac and dc magnetoresistances can be tuned from almost zero to 108% by varying the bias. To explain the diversity of magnetotransport phenomena observed in the Mn/SiO2/p-Si structure, it is necessary to attract several mechanisms, which possibly work in different regions of the structure. The anomalously strong magnetotransport effects are attributed to the magnetic-field-dependent impact ionization in the bulk of a Si substrate. At the same time, the conditions for this process are specified by structure composition, which, in turn, affects the current through each structure region. The effect of magnetic field attributed to suppression of impact ionization via two mechanisms leads to an increase in the carrier energy required for initiation of impact ionization. The first mechanism is related to displacement of acceptor levels toward higher energies relative to the top of the valence band and the other mechanism is associated with the Lorentz forces affecting carrier trajectories between scatterings events. The estimated contributions of these two mechanisms are similar. The proposed structure is a good candidate for application in CMOS technology-compatible magnetic- and electric-field sensors and switching devices.