Classical thermoelastic damping (TED) model faces significant challenges due to micro- and nano- fabrication technology led to the rapid reduction in the size of resonators. This study aims to evaluate the effects of both mechanical small size effect and thermal small size effect on the TED of micro- and nano-scale axisymmetric vibration circular plate resonator. Based on the Kirchhoff plate theory, a TED model is first established that simultaneously considers the surface effect and the dual-phase-lag (DPL) heat conduction model. Analytical solution of the TED model under various boundary conditions is obtained using the complex frequency method. The analytical solution is theoretically validated. The numerical results demonstrate that the combined effect of both small size effects is confined within a limited range. This research can provide new theoretical guidance for the optimization design of high-quality micro- and nano-scale axisymmetric circular plate resonators.