Connections are recognized as the most critical components in structural systems for transferring loads and maintaining overall integrity under various static and dynamic loading conditions. Replaceable energy-dissipating structural fuses provide an effective means of protecting structures against earthquake forces. However, previous studies have identified two major challenges: the dependence of the cyclic performance of yielding fuses on beam-section dimensions and the risk of damage to primary load-bearing members. To overcome these limitations, this study proposes an innovative pin-jointed connection that converts beam rotation into yielding of a replaceable damper, thereby concentrating damage exclusively in a designated region. This mechanism protects the beam and column while simultaneously making the cyclic response of the connection independent of beam-section dimensions. First, the seismic behavior of three yielding mechanisms—flexural, shear, and ADAS dampers—was experimentally compared under cyclic loading. Owing to the superior performance of the ADAS damper, the numerical model of the connection was then validated, and a parametric study was conducted on 12 models by varying the damper’s minimum width and thickness to systematically evaluate their effects on the seismic response. The results showed that the ADAS damper reached a final rotation of 0.08 rad and provided notably greater ductility and energy-dissipation capacity than the other specimens. Increasing the damper width and thickness enhanced the connection stiffness, maximum moment, and absorbed energy. Finally, the evaluation of beam-section dimensions showed that, when the force-transfer arm remained constant, changing the beam size had no significant effect on the cyclic response of the connection.