A magnetically controlled elastically driven electroporation phenomenon, or magneto-elasto-electroporation (MEEP), is discovered while studying the interactions between core-shell magnetoelectric nanoparticles (CSMEN) and biological cells in the presence of an a.c. magnetic field. In this paper we report the effect of MEEP observed via a series of in-vitro experiments using core (CoFe2O4)-shell (BaTiO3) structured magnetoelectric nanoparticles and human epithelial cells (HEP2). The cell electroporation phenomenon and its correlation with the magnetic field modulated CSMEN are described in detail. The potential application of CSMEN in electroporation is confirmed by analyzing crystallographic phases, multiferroic properties of the fabricated CSMEN, influences of d.c. and a.c. magnetic fields on the CSMEN and cytotoxicity tests. The mathematical formalism to quantitatively describe the phenomena is also reported. The reported findings provide insights into the underlying MEEP mechanism and demonstrate the utility of CSMEN as an electric pulse-generating nano-probe in electroporation experiments with a potential application toward accurate and efficient targeted cell permeation.