Western Mexico, where the young and small Rivera Plate and the adjacent large Cocos Plate are subducting beneath the North American Plate, is a unique region on Earth where tearing of subducting oceanic plates, as well as fragmentation of the overriding continental plate, is occurring today. Characterizing the mantle flow field that accompanies the subduction of the Rivera and adjacent Cocos plates can help to clarify the tectonics and magma genesis of this young plate boundary. Here we report observations of seismic anisotropy, as manifested by shear wave splitting derived from local S and teleseismic SKS data collected by the Mapping Rivera Subduction zone array that was deployed from 2006 January to 2007 June, in southwestern Mexico, and from data collected by two of Mexico's Servicio Sismológico Nacional stations. SKS and local S-wave splitting parameters indicate that the fast directions of the split SKS waves for stations that lie on the central and southern Jalisco Block are approximately trench-normal, following the convergence direction between the Rivera Plate and Jalisco Block. S-wave splitting from slab events show a small averaged delay time of ~0.2 s for the upper 60 km of the crust and mantle. Therefore, the main source of anisotropy must reside in the entrained mantle below the young and thin Rivera Plate. Trench-oblique fast SKS split directions are observed in the western edge of the Rivera Plate and the western parts of the Cocos slab. The curved pattern of fast SKS split directions in the western Jalisco block and beneath the Rivera-Cocos slab gap indicates 3-D toroidal mantle flow, around the northwestern edge of the Rivera slab and the Rivera-Cocos gap, which profoundly affect the finite strain field in the northwestern edge of the Rivera slab and the mantle wedge. Both the tomographic images and shear wave splitting results support the idea that the Rivera and western Cocos plates not only moved in a downdip direction but also have recently rolled back towards the trench and that the Colima rift is intimately related to the tearing between the Rivera and Cocos plates.