A chaser satellite equipped with robotic arms can capture space debris and manipulate it for use in more advanced missions such as refueling and deorbiting. To facilitate capturing, a caging-based strategy has been proposed to simplify the control system. Caging involves geometrically constraining the motion of the target debris, and is achieved via position control. However, if the target is spinning at a high speed, direct caging may result in unsuccessful constraints or hardware destruction; therefore, the target should be de-tumbled before capture. To address this problem, this study proposes a repeated contact-based method that uses impedance control to mitigate the momentum of the target. In this study, we analyzed the proposed detumbling technique from the perspective of impedance parameters. We investigated their effects through a parametric analysis and demonstrated the successful detumbling and caging sequence of a microsatellite as representative of space debris. The contact forces decreased during the detumbling sequence compared with direct caging. Further, the proposed detumbling and caging sequence was validated through simulations and experiments using a dual-arm air-floating robot in two-dimensional microgravity emulating testbed.