Studies with transplanted tumors in animals and clinical trials have provided the proof-of-concept of magnetic hyperthermia (MH) therapy of cancers using iron oxide nanoparticles. Interestingly, in several studies, the application of an alternating magnetic field (AMF) to tumor cells having internalized and accumulated magnetic nanoparticles (MNPs) into their lysosomes can induce cell death without detectable temperature increase. To explain these results, among other hypotheses, it was proposed that cell death could be due to the high-frequency translational motion of MNPs under the influence of the AMF gradient generated involuntarily by most inductors. Such mechanical actions of MNPs might cause cellular damages and participate in the induction of cell death under MH conditions. To test this hypothesis, we developed a setup maximizing this effect. It is composed of an anti-Helmholtz coil and two permanent magnets, which produce an AMF gradient and a superimposed static MF. We have measured the MNP heating power and treated tumor cells by a standard AMF and by an AMF gradient, on which was added or not a static magnetic field. We showed that the presence of a static magnetic field prevents MNP heating and cell death in standard MH conditions. The heating power of MNPs in an AMF gradient is weak, position-dependent, and related to the presence of a non-zero AMF. Under an AMF gradient and a static field, no MNP heating and cell death were measured. Consequently, the hypothesis that translational motions could be involved in cell death during MH experiments is ruled out by our experiments.