Remote control of cells and single molecules by magnetic nanoparticles in nonheating external magnetic fields is a perspective approach for many applications such as cancer treatment and enzyme activity regulation. However, the possibility and mechanisms of direct effects of small individual magnetic nanoparticles on such processes in magneto-mechanical experiments still remain unclear. In this work, we have shown remote-controlled mechanical dissociation of short DNA duplexes (18-60 bp) under the influence of nonheating low-frequency alternating magnetic fields using individual 11 nm magnetic nanoparticles. The developed technique allows (1) simultaneous manipulation of millions of individual DNA molecules and (2) evaluation of energies of intermolecular interactions in short DNA duplexes or in other molecules. Finally, we have shown that DNA duplexes dissociation is mediated by mechanical stress and produced by the movement of magnetic nanoparticles in magnetic fields, but not by local overheating. The presented technique opens a new avenue for high-precision manipulation of DNA and generation of biosensors for quantification of energies of intermolecular interaction.