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Laguerre–Gaussian beams with vortex structure, as a special type of electromagnetic wave, can carry energy, momentum, and angular momentum, which is crucial for understanding of dynamical processes concerning light–matter interaction phenomena. In this paper, we theoretically investigate the local dynamical characteristics of Laguerre–Gaussian vortex beams upon reflection and refraction. Using a hybrid method based on the angular spectrum representation and vector potential in the Lorenz gauge, the explicit analytical expressions for the electric and magnetic field components of reflected and refracted Laguerre–Gaussian beams are derived in the form of a Hermite polynomial. A canonical approach is utilized to examine the energy, momentum, and spin and orbital angular momentum of the Laguerre–Gaussian vortex beams’ reflection and refraction at a plane interface between air and BK7 glass. The effects of the incidence angle, topological charge, and polarization state on these dynamical quantities are simulated and discussed in detail. This study may provide useful insights into the interactions of vortex beams with matter and their further applications.