The current-carrying arc is a critical factor that affects the electrical contact performance and material damage of contact pairs. In this study, a copper disk–copper disk pair was used to simulate the rolling electrical joint in a conductive rotating joint. Under operating conditions with a current of 2 A, rotation speeds from 4 to 600 r/min, and loads from 40 to 180 N, the dynamic behavior of the current-carrying arc and the surface damage mechanism were investigated. The movement characteristics of the arc at the friction interface were observed, and the arc generation difficulty and intensity were statistically analyzed based on the arc burning rate and arc energy. With increasing load and rotation speed, the generation of current-carrying tribological arcs became easier, and both the arc burning rate and arc energy increased. After the arc was generated, the arc root position was randomly distributed at the contact interface, exhibiting dynamic phenomena such as splitting and merging. Following the generation of the arc, the dominant damage mechanism at the current-carrying friction interface transitioned from mechanical damage to electrical damage. The manifestations of electrical damage included burning, oxidation, and roughening, with the degree of electrical damage positively correlated with the arc burning rate and arc energy. Surface oxidation could reduce the adhesion between metal contact pairs, contributing to a decrease in the current-carrying friction coefficient. Simultaneously, the film resistance caused by oxidation and the contraction resistance caused by roughening could lead to an increase in the average contact resistance.