The dynamics of C(3P) + Si2(X $^{3}\Sigma ^-_g$) → Si(3P) + SiC(X 3Π) on its ground state Si2C(X 1A1) are of great significance in carbon-rich interstellar chemistry. Using the combined-hyperbolic-inverse-power-representation method, we construct the first global potential energy surface (PES) for the electronic ground state Si2C(X 1A1) based on a total of 4080 ab initio energy points, which are obtained at the Davidson-corrected internally contracted multireference configuration interaction level of theory. The topographical features of the newly constructed PES are examined in detail and show good agreement with previous theoretical and experimental studies. Finally, we investigate the C(3P) + Si2(X $^{3}\Sigma ^-_g$) → Si(3P) + SiC(X 3Π) reaction using the quasi-classical trajectory and time-dependent wave packet calculations, yielding reasonable integral cross sections and rate constants, which are expected to be useful for astrochemical modelling in carbon-rich interstellar environments.