BiFeO₃ (BFO) thin films were epitaxially grown on a 0.7 wt% Nb-doped (001) SrTiO₃ (NSTO) single-crystal substrate by pulsed laser deposition to form a Pt/BFO/NSTO heterostructure. This heterostructure exhibits stable bipolar resistive switching behavior with a maximum R_off/R_on ratio of 10⁵, well retention and multilevel memory properties. Meanwhile, the saturation magnetization (M_s) of BFO film shows reversible switching upon different resistance states. The BFO film shows high saturation magnetization at a high resistance state, while it shows low saturation magnetization at a low resistance state. These resistive and magnetization switching properties are attributed to the modulation effect of the ferroelectric polarization reversal on the width of depletion region and the height of potential barrier via the charge trapping and detrapping process combined with the migration of oxygen vacancies at the BFO/NSTO interface. This study demonstrates that Pt/BFO/NSTO heterostructure has potential application in nonvolatile resistive switching memory and novel magnetoelectric coupling devices.