The role of the properties of magnetic nanoparticles in the remote magneto-mechanical actuation of biomolecules under the influence of external magnetic fields is still of particular interest. Here, a specially designed strategy based on the mechanical destruction of short oligonucleotide duplexes is used to demonstrate the effect of magnetic nanoparticles with different sizes (5-99 nm) on the magnitude of the magneto-mechanical actuations in a low-frequency alternating magnetic field. The results show that the mechanical destruction of complementary chains of duplexes, caused by the rotational-vibrational movements of nanoparticles upon exposure to a magnetic field, has a nonmonotonic dependence on the nanoparticle core size. The main hypothesis of this phenomenon is associated with a key role of magneto-dipole interactions between individual nanoparticles, which blocks the movements of nanoparticles in dense clusters. This result will allow fine-tuning of the magnetic nanoparticle properties for addressing specific magneto-mechanical tasks.