The stability of ion-conductive membranes, such as perfluorosulfonic-acid (PFSA) membranes, as a solid-electrolyte separator in energy devices is strongly linked to their mechanical properties, the characterization of which presents challenges, especially in the presence of ionic interactions. Ionomer membranes' elastic properties are affected by cations; however, their influence on deformation at small and large strains is relatively unexplored. In this paper, we report the stress-strain response and fracture behavior of Nafion membranes exchanged with various cations examined in three deformation regimes. In the small-strain regime, the Young's modulus is strongly dependent on cation size, due to the reduced mobility and local stiffening of polymer chains. The Young's modulus, yield limit and strain-hardening modulus all increase with monovalent cation size in the order H+ < Li+ < Na+ < K+ < Cs+, but with varying dependence. In the failure regime, however, the break strain and fracture energy of the membrane decrease in the presence of larger cations, which promote deformation instability while decreasing plastic dissipation energy during crack propagation, thereby leading to more brittle fracture. These results not only demonstrate the trade-off between strength and fracture toughness, but also reveal how it is altered by the ionic interactions, which also dictate the inverse relationship between stretchability and stiffness. Moreover, the measured stress-strain data are reproduced by the constitutive relations to extract parameters that are correlated to the fracture energy through craze instability. Such relationships provide insight into how parameters extracted from tensile testing can be used to assess membrane stability and the role of ionic interactions.