The present study investigates the dynamic behavior of rotating sandwich beams with variable thickness, consisting of an auxetic core (either extensional or high-damping elastomeric) and metallic face sheets. Such structures are increasingly employed in aerospace, automotive, and advanced rotating tool applications. The modeling is carried out using higher-order shear deformation theory, and the governing equations are derived via Hamilton’s principle and solved using the generalized differential quadrature method. Numerical results indicate that increasing the angular velocity leads to a pronounced rise in natural frequencies due to the centrifugal stiffening effect, whereas increasing the tapering parameter results in a reduction of the frequencies owing to the decrease in bending stiffness. In addition, increasing the aspect ratio of the auxetic cell dimensions and decreasing the cell re-entrant angle significantly enhance the natural frequencies. The choice of different metals for the face sheets also has a notable influence on the vibrational response, with steel providing the greatest increase in natural frequency. These findings not only contribute to a deeper understanding of the vibrational behavior of auxetic structures under rotational conditions, but also facilitate the design of advanced systems in the aforementioned industries.