Recently, we have reported that polyampholytes, synthesized from free radical copolymerization of anionic monomer and cationic monomer, form physical hydrogels of high toughness and self-healing. The random distribution of the opposite charges forms ionic bonds of a wide distribution of strength. The strong bonds serve as permanent cross-links, imparting elasticity, whereas the weak bonds serves as reversible sacrificial bonds by breaking and reforming to dissipate energy. In this work, we focus on the rupture behaviors of the polyampholyte physical hydrogel, P(NaSS-co-MPTC), copolymerized from sodium p-styrenesulfonate (NaSS) and 3-(methacryloylamino)propyltrimethylammonium chloride (MPTC). Tensile test and pure shear test were performed at various stretch rates in the viscoelastic responses region of the material. Tensile test showed yielding, strain softening, and strain hardening, revealing the dually cross-linked feature of the gel. Pure shear test showed crack blunting at the notched tip and a large yielding zone with butterfly shaped birefringence pattern ahead of the crack tip. After blunting, crack advanced at steady-state velocity with a constant angle. The conditions for the occurrence of crack blunting and variables governing the crack advancing angle are discussed. We found that even for these highly stretchable samples, significant blunting only occurs when the tensile fracture stress sigma(f) is larger than modulus E by a factor of about 2, in consistent with Huis theoretical prediction for elastic materials. The crack advancing angle theta was found to be proportional to sigma(y)/E over a wide stretch rate range, where sigma(y) is the yielding stress. In addition, the fracture energy was correlated to small strain modulus by a power law in the viscoelastic response region. This systematic study will merit revealing the fracture mechanism of tough viscoelastic materials including biological tissues and recently developed tough and highly stretchable hydrogels.