As the counterpart in the lower frequencies of localized surface plasmon (LSP) in the optical regime, spoof LSP has attracted great interest among researchers due to its notable properties such as deep-subwavelength field localization and high-Q-value resonance. Microwave plasmonic resonators (MPRs) that hold several geometric symmetries are a typical device to generate spoof LSP modes. Several methodologies have been developed to study the mode responses of the MPRs, such as effective medium theory and equivalent dispersion theory. However, both of the theories are based on the assumptions that do not properly consider the geometric symmetries held by the MPRs, resulting in which they cannot completely reveal the mode properties of the MPRs. In this paper, a methodology based on group representation theory is proposed to analyze how the geometric symmetries affect the mode responses of the MPRs. By employing symmetry arguments, it is found that the azimuthal orders of the spoof LSP modes are totally determined by the irreducible representations (irreps) of the group composed by the geometric symmetries of the MPRs. The number of the irreps is equal to the number of the spoof LSP modes. A MPR holding C7v group symmetry is taken as an example to explain our methodology. The C7v group only has five irreps (three doubly-degenerate and two nondegenerate irreps). Therefore, the MPR can only support five spoof LSP modes with different azimuthal orders, i.e., zero-order mode (also known as magnetic dipole), dipole, quadrupole, hexapole and quattuordecpole. The dipole, quadrupole and hexapole modes are related to three doubly-degenerate irreps implying that the three modes are doubly degenerate. The zero-order and quattuordecpole modes correspond to the two nondegenerate irreps respectively and thus are nondegenerate. The MPR with C7v group symmetry cannot support more spoof LPS modes limited by its geometric symmetries. A MPR prototype with C7v group symmetry is designed and simulated. The full-wave simulation results well demonstrate our methodology. Although proposed to analyze the mode responses of the MPRs, our methodology is widely applicable and can also be used to analyze the mode responses of the plasmonic resonators working in other frequency bands like the optical band.