This paper presents an investigation on the cyclic behavior and design aspects of a hybrid self-centering wall (SW), in terms of the wall’s axial stress and post-tensioning tendons’ prestressing ratios. These key parameters are examined extensively within the context of both force and displacement-based design approaches. Finite element models of SWs are developed and verified against experimental results available from the literature. The numerical model is used to perform a parametric study where the wall’s behavior, including cyclic response, damage severity and pattern, energy dissipation, stiffness degradation, period shift, and residual drift are widely discussed in the context of the aforementioned design approaches. Numerical results indicate that an increase in the axial stress ratio intensifies the extent and severity of the wall’s damage, lateral capacity, residual drift, energy dissipation, and structural seismic demand. Additionally, it is shown that by increasing the tendons’ prestressing ratio, the structural seismic demand is increased, while the wall’s damage, residual drift, and energy dissipation capacity are decreased. Based on this study, the wall’s axial stress ratio and the tendons’ prestressing ratio should be limited to a range of 0.075–0.115 and less than 0.75, respectively, to meet the basic objective performance. Higher objective performance criteria could be maintained with using external energy dissipaters, and adopting a suitable design approach.