The manipulation of magnetic nanoparticles (MNPs) using an external magnetic field, has been successfully demonstrated in various biomedical applications. Some have utilised this non-invasive external stimulus and there is an potential to build on this platform. The focus of this study is to understand the manipulation of MNPs by a time-varying static magnetic field and how, at different frequencies and displacement, this can alter cellular function. Here we explore, using numerical modeling, the physical mechanism which underlies this process, and we discuss potential improvements for its use in biomedical applications. From our data and other related studies, we infer that such phenomenon largely depends on the magnetic field gradient, magnetic susceptibility and size of the MNPs, magnet array oscillating frequency, viscosity of the medium surrounding MNPs, and distance between the magnetic field source and MNPs. Additionally, we demonstrate cytotoxicity in neuroblastoma (SH-SY5Y) and hepatocellular carcinoma (HepG2) cells in vitro induced by MNPs exposed to a magnetic field gradient and oscillating at various frequencies and displacement amplitudes. Even though this technique reliably produces MNP endocytosis and/or cytotoxicity, a better understanding is required to develop this system for precision manipulation of MNPs, ex vivo.