We demonstrate the coexistence of the unipolar and bipolar switching behaviors in a single oxide resistive device composed of Pt-CuO0.8-W structure and we reveal the switching mechanism by the comprehensive analyses of both unipolar and bipolar switching behaviors. The observations suggest that the RESET (turning OFF) mechanism of unipolar and bipolar switching modes can be explained by a unified scheme. The results also elucidate that the SET (turning ON) process in bipolar mode is originated from by the drift of ions though charged vacancies, while the SET process in unipolar mode is explained by electron tunneling through vacancies. The proposed model successfully explains the observations of resistive switching of our device regardless of input voltage polarity and, more importantly, we propose a way to selectively choose one specific operation mode.