Radiofrequency cavities play a crucial role in synchrotron light sources by replenishing beam energy and providing sufficient accelerating voltage. Compared to traditional TM010 cavities, TM020 cavities offer advantages such as higher quality factor, higher accelerating voltage, and lower characteristic impedance. Additionally, their unique field distribution allows strategic placement of dampers at radial nodes, effectively suppressing higher-order modes within a compact structure. However, the radiofrequency performance of cavity is highly sensitive to the placement of the higher-order modes coupling slot and the Electromagnetic(EM) field symmetry. These factors can easily lead to leakage of the accelerating mode, with the leaked energy absorbed by the absorber, whose power handling capacity is limited. Consequently, the leakage rate of the TM020 mode damping cavity becomes critical in limiting the achievable accelerating cavity voltage. This paper proposes a novel extraction scheme utilizing a circular waveguide structure and a waveguide-coaxial input coupler to significantly reduce accelerating field leakage, thereby achieving a high-fidelity TM020 cavity. A detailed design of a 500 MHz TM020 HOM-damped cavity is presented. Simulation results demonstrate that the energy leakage of the accelerating mode can be suppressed below 1% during operation.