Cordilleran orogens, such as the central Andes, form above subduction zones, and their evolution depends on both continental shortening and oceanic plate subduction processes, including arc magmatism and granitoid batholith formation. Arc and batholith magma compositions are consistent with partial melting of continental lithosphere and magmatic differentiation, whereby felsic melts rise upward through the crust, leaving a high-density pyroxenite root in the deep lithosphere. We study gravitational removal of this root using two-dimensional thermal-mechanical numerical models of subduction below a continent. The volcanic arc position is determined dynamically based on thermal structure, and formation of a batholith-root complex is simulated by changing the density of the arc lithosphere over time. For the model lithosphere structure, magmatic roots with even a small density increase are readily removed for a wide range of root strengths and subduction rates. The dynamics of removal depend on the relative rates of downward gravitational growth and lateral shearing by subduction-induced mantle flow. Gravitational growth dominates for high root densification rates, high root viscosities, and low subduction rates, resulting in drip-like removal as a single downwelling over 1-2.5 m.y. At lower growth rates, the root is removed over >3 m.y. through shear entrainment as it is carried sideways by mantle flow and then subducted. In all models, >80% of the root is removed, making this an effective way to thin orogenic mantle lithosphere. This can help resolve the mass problem in the central Andes, where observations indicate a thin mantle lithosphere, despite significant crustal shortening and thickening.