The origin of the anomalous low-temperature staircase-like magnetization behavior in magnetic shape memory alloys, which has been commonly observed in a large variety of materials, has been remaining a mystery since it was discovered. Here, we elucidate the underlying mechanism for such anomalous magnetic behavior via tracing the structural evolution during applying magnetic fields at 4 K in an archetypal Ni-Mn-based magnetic shape memory alloy, by in-situ neutron diffraction technique. We found that it is the magnetic-field-induced structural transformation occurring at this extremely low temperature (far below martensitic transformation temperature) that is responsible for the anomalous low-temperature magnetic behavior. It is believed that this transformation proceeds by a succession of discrete steps, accounting for the abrupt jumps on the magnetization curve. The present study provides deep insights into the interplay between magnetism and structure in magnetic shape memory alloys, and it is also instructive for understanding the anomalous staircase-like magnetization behavior in other materials undergoing a magnetostructural transition.