Graphene, a one-atom-thick layer of carbon atoms arranged in a hexagonal honeycomb lattice, has attracted intensive attention and extensive investigation because of its striking electronic and optical properties. Especially, the reflection coefficients of graphene are determined by the fine structure constant and intrinsic parameters, which can be tuned by altering the Fermi level. Such interesting feature makes graphene a good candidate for tuning the optical properties of structured light. On the other hand, structured light beams with vortex phase have become a research hotspot in optics and optoelectronics due to their unique physical properties and novel physical effects, as well as various promising potential applications. It is well known that the complex amplitude of a vortex beam comprises a phase$\mathrm{e}\mathrm{x}\mathrm{p}\left(\mathrm{i}l\phi \right)$, where$l$is an integer often called the topological charge and$\phi$is the azimuthal angle. A common example of the vortex beams is the Laguerre-Gaussian (LG) beams. As a special type of electromagnetic wave, the LG vortex beams can carry energy, momentum, and angular momentum, which can be classified into Spin Angular Momentum (SAM) and Orbital Angular Momentum(OAM). As well known, energy, momentum, SAM, and OAM are the main dynamical characteristics of light and play a crucial role in understanding the light-matter interactions. There has been a recent study on the dynamical characteristics of vortex beams reflected from an air-glass interface. However, to the best of our knowledge, the local dynamical characteristics of vortex beams reflected from a graphene-substrate interface have not been reported. Compared to the conventional air-glass interface, graphene-substrate interface may reveal many other important and interesting features of the vortex beams upon reflection. Meanwhile, the dynamical characteristics of reflected vortex beams are of great importance in understanding the optical properties of graphene. In this work, we investigate the dynamical characteristics of the vortex beams impinging on graphene-substrate surfaces. Firstly, the Fresnel reflection coefficients of the graphene-substrate system in the presence of an imposed magnetic field are briefly given. The proposed expressions of the Fresnel reflection coefficients are characterized by the parameters of refraction angle, permittivity of the substrate, permittivity and permeability in vacuum, and the longitudinal, transverse and Hall conductivities. Among these parameters, the Hall conductivity, a very important parameter of the graphene-substrate system, is quantized in multiples of the fine structure constant and is described by the number of occupied Landau levels, the imposed magnetic field, the Fermi energy and the Fermi velocity. Then, a theoretical model that takes into full account the vectorial nature of electromagnetic fields is established to describe the LG vortex beams reflected from a graphene-substrate interface. In this model, starting from the expression of the vortex beam on the initial plane in the source plane and utilizing the Fourier transform, the angular spectrum amplitude of the LG vortex beam is obtained. The angular spectrums of the reflected beam are related to angular spectrums of the incident beam by means of a matrix considering boundary conditions and Taylor series expansion. Utilizing the angular spectrum representation, the horizontal and vertical components of the reflected LG vortex beam are derived. Further, introducing vector potential and using a Lorenz gauge, the explicit analytical expressions for the electric and magnetic field vectors of the reflected LG vortex beam are obtained. Based on the derived formulas, the energy, momentum, SAM, and OAM of the LG vortex beams reflected from a graphene-substrate interface are examined. The effects of the incidence angle, topological charge, Fermi energy, and magnetic field on these dynamical quantities are analyzed. The results show that the energy, momentum, SAM, and OAM density distributions change abruptly near the Brewster angle. With the increasing of topological charge, the distributions of these dynamical quantities in the transverse plane gradually go away from the center and the peak position changes greatly. When the incident angle is small, the Fermi energy and magnetic field have little effect on the energy density of the reflected vortex beam. When the incident angle is greater than a certain angle, which is $\mathrm{50}°$ for the case considered, the greater the Fermi energy or the smaller the magnetic field, the greater the energy density. The momentum and OAM density distributions show a similar trend with the change of Fermi energy and magnetic field. When ${\theta }_{\mathrm{i}}<\mathrm{70}°$, the smaller the Fermi energy or the larger the magnetic field, the smaller the momentum and OAM densities. As the incident angle increases, the SAM density first decreases gradually, reaches its minimum value, and then increases rapidly. The larger the Fermi energy or the smaller the magnetic field, the larger the incident angle corresponding to the minimum value of the SAM density. These findings lay a foundation for the characterization of graphene based on the local dynamical characteristics of vortex beams, and are of great significance for promoting the theoretical and applied research on the tunable optical properties of vortex beam with graphene.