In recent years, Laguerre-Gaussian (LG) laser beams have gained significant attention in plasma physics due to their unique vortex characteristics. However, laser spots generated in experimental settings often deviate from a perfectly circular profile. Based on the Nonlinear Schrödinger Equation (NLSE) governing laser propagation in underdense plasmas, our study investigates the influence of spot ellipticity on the filamentation instability of LG beams. By solving the NLSE using the Split-Step Fourier Method (SSFM), we can characterize the propagation properties of the elliptical LG beams under various parameters in underdense plasmas. Numerical simulations show that when the incident power is below the critical power for self-focusing, the spot rotates by a certain angle depending on the sign of the topological charge of the vortex beam. Then it gradually evolves into the neighboring ground state of the Helmholtz equation, a Vortex Hermite-Gaussian (VHG) beam. This evolution occurs over a distance approximately equal to the elliptical Rayleigh length. When the incident power exceeds the critical power, the elliptical spot with broken symmetry causes the plasma refractive index gradient to be directed toward the sides of the major axis, leading to the lateral migration of self-focused energy along this axis. Consequently, filaments mainly distribute along the major axis, forming earlier than in other regions and potentially exhibiting merging phenomena. At powers slightly above the critical power, only two filaments form. Furthermore, filamentation is classified into two cases based on the relationship between the self-focusing distance and the evolution distance. We also refined the azimuthal modulation instability theory and derived a modified expression for the critical power of elliptical LG beams. When the self-focusing distance is smaller than the evolution distance, the number of filaments obtained from simulations is consistent with theoretical predictions. These findings highlight the significant differences in propagation characteristics between elliptical and ideal LG beams due to symmetry breaking, providing crucial insights for the theoretical application and experimental study of ultra-intense laser beams.