The reflection and transmission of a Bessel vortex beam incident on a stratified uniaxial anisotropic slab are analytically solved by use of the expansion of cylindrical vector wave functions (CVWFs). This work is an extension of our previous paper, in which the reflection and transmission of a Bessel vortex beam incident on a homogeneous uniaxial anisotropic slab were studied. A closed form of the expansion coefficients of the reflected and transmitted beams for a stratified slab is derived. Taking a three-layered uniaxial anisotropic slab as an example, the characteristics of the reflected and transmitted beams and its influencing factors are numerically analyzed, including the magnitude profiles of the electric field components, the energy conversion between the two transverse electric components, and the distortion of orbital angular momentum (OAM) states. The results indicate that the effects of the dielectric properties of each layer on the magnitude profiles of the reflected field components are prominent, while those of the transmitted beams are opposite, which could be applied in the design of optical devices. Compared with other polarization modes, the polarization perturbation for the circularly polarized caseis very slight. As for the oblique incidence, an increase of the incident angle can obtain a high-quality reflected beam with fewer derived OAM states, and the lossy media can also do the same. Since the uniaxial anisotropic media has many applications in optical communication, radar detection, microwave device manufacture, etc., and vortex beams are proved to increase the channel capacity of an optical communication systems, these numerical results are of use in optical communications, for example, reducing the crosstalk in optical communication.