This paper introduces a novel type of connection that integrates unbonded prestressed strands (UPS) and mortise-tenon in an assembly frame structure (UPS-MTF). First, the damage process and failure modes of the joints under reciprocating horizontal loads were systematically analyzed using refined numerical models. The recommended values of the design parameters of the joints were derived from the parametric analysis results. Refined numerical modeling results reveal the diagonal compression strut mechanism within the core region of the joint. The diagonal compression struts model assists in establishing the theoretical calculation formula for the skeleton curve of shear stress–strain in the core region. Second, a genetic algorithm (GA) parameter was identified for the restoring force model of the core region to determine the parameters of the hysteresis rules. Finally, a macro-simplified analytical model of the joint was created based on the restoring force model of the core region, and parameter analysis was conducted to verify the applicability of this macro-simplified analytical model. The research results prove that the damaged form of the joint proposed in this paper originates from the shear and relative slip damage between the components in the core region. The axial compression ratio significantly affects the hysteretic performance of the joints, and the upper and lower limit values were identified for the axial compression ratio of the joints. The area and initial effective stress of the UPS exert a minimal effect on the hysteretic performance of the joint. Based on the method proposed in this paper for determining the restoring force model in the core region of the joints, the hysteresis curves obtained from the macro-simplified analytical model closely match the refined numerical analysis model results. This correspondence verifies the applicability of the macro-simplified analytical model.