Quench protection has always been challenging for high-temperature superconductor (HTS) coils. Fast current discharge after quench detection is important for a successful coil protection. The copper plates initially intended for cooling can significantly accelerate the discharging process for HTS coils through electromagnetic coupling between coils and copper plates. However, the underlying physical mechanism of this technique has not been studied thoroughly. Here we present a detailed study on the electromagnetic and thermal characteristics of HTS coils coupled with copper plates through experiments and simulations. The results show that a considerable current rebound occurs after an accelerating current drop in the early stage of the fast-discharging process. This coil current rebound is induced by temperature rise as well as the resistivity of copper plates, which are heated by induced eddy current. The heat transfer from copper plates can uniformly heat the whole coil rapidly, which speeds up the discharging process, meanwhile it can also induce overcurrent quench risk. A 30 T@20 K HTS magnet with 36 single pancakes (SP) is analyzed. The coupling copper plates can make the coil current drop to 36.9% within the initial 8 ms. The temperature rise induced by copper plates shows a considerable nonuniform distribution among the multiple coil systems. The protection can be enhanced by optimizing the resistivity of copper plates and magnetic coupling strength between plates and coils. This technique has great potential for the protection of insulated HTS magnets.