The control of light-matter interaction in metasurfaces offers an unexplored potential for the excitation and manipulation of light. Here, we combine experimental terahertz time-domain spectroscopy and near-field scanning terahertz microscopy to demonstrate the role of reciprocal vectors in the transmission and plasmonic resonances of quasicrystal metasurfaces. An investigation of two-dimensional metasurface structures with different rotationally symmetric quasicrystal arrangements demonstrates that the transmission minima resulting from Wood's anomaly are directly related to the surface plasmon resonances. We also find that the surface plasmon resonances of the quasicrystal metasurface were determined by the reciprocal vectors, which could be well explained by the coupling condition of the resonances, and the characteristic frequencies remain un-shifted under various slit sizes. Our findings demonstrate a new potential in developing novel plasmonic metasurfaces.