Non-Asbestos Organic (NAO) is widely used in automobile braking systems due to its low cost and stable performance. Meanwhile, NAO is also suitable for seismic energy dissipation of building structures, but further research was required. Configuration and loading rate are significant factors affecting the hysteretic performance of the friction damper. Thus, cyclic loading tests were conducted to evaluate the friction behavior of friction dampers with non-metallic friction pads (Non-Asbestos Organic (NAO) and Polytetrafluoroethylene (PTFE)), and the friction pairs were NAO-Steel and PTFE-Steel, respectively. A total of 13 specimens were designed to comparatively analyze the effects of the following factors on the mechanical performance of the friction damper: the configuration of the friction damper, loading rate, and reloading process after a reassembly. Firstly, some unnecessary friction needed to be avoided to keep the stable performance of the damper, such as the contact friction between the slot of the inner steel plate and friction pads or bolts. Secondly, the normal force of both NAO and PTFE friction dampers reduced gradually during the loading process. The former showed a higher cumulative loss rate, which increased with the initial nominal pressure. Again, the dynamic friction coefficients of NAO and PTFE friction dampers tended to be constant under high-speed loading, which was remarkably higher than that under low-speed loading. The dynamic friction coefficients of NAO and PTFE friction dampers were suggested to be 0.229 and 0.121 for structural analysis, respectively. Finally, compared with the first test of the friction damper, the reloading test results after a reassembly showed excellent reusability of both NAO and PTFE friction dampers.