Peeling an adhesive tape exhibits dynamic stick-slip instabilities, which are typically observed within a specific range of peel speeds. We demonstrate that this stick-slip instability arises from the viscoelastic dynamics of discrete fibrils formed during adhesive deformation and that a transition occurs from strength-governed to energy-governed fracture throughout the stickslip process. By systematically tuning the adhesives/substrate detaching response, we show that the stick-slip instability can occur even at very low peel speeds, a phenomenon previously thought to be restricted to higher speeds. This work provides a deeper understanding of the physics behind stick-slip behavior in peeling, offering potential strategies for mitigating this instability in practical applications.