The Sierra Madre Occidental (SMO) of western Mexico is one of the largest silicic volcanic provinces on Earth, but the mechanism for the generation of such a large volume of ignimbrites has never been clearly defined. We present new 40Ar/39Ar ages, geologic mapping, and structural data for the southern part of the SMO demonstrating that most of this volcanic province was built in two episodes of ignimbrite flare-up in Oligocene (31.5--28 Ma) and early Miocene (23.5--20 Ma) time, and that extensional deformation occurred mostly before the transfer of Baja California to the Pacific plate. Extensive ignimbrite successions, with 40Ar/39Ar ages clustering at ~23 and ~21 Ma, cover most of the southern SMO, thus correlating in age with ignimbrites exposed in southern Baja California and central Mexico. Grabens with a 020¿ to N-S orientation developed in the east almost concurrently with this volcanic episode. Half grabens and NNW striking listric normal fault systems formed at the end of middle Miocene as far as 150 km from the present coast. A belt of left-lateral transpressional structures formed along the southern boundary of the SMO during the same period. We link these magmatic and tectonic events to the evolution and dynamics of the Farallon and North America plates during the Miocene. Particularly, we propose that a first detachment of the lower part of the Farallon plate in early Miocene time produced a transient thermal event and partial melting of the crust via mafic underplating. Middle Miocene extension would be related to a second detachment event, resulting from the slowing subduction that preceded the final capture of the Magdalena microplate by the Pacific plate at 12.5 Ma. Transpression at the southernmost end of the SMO occurred along the inland projection of the Magdalena-Cocos plate boundary and may be explained by a difference in subduction rate and by a temporal convergence between the two plates in the eve of the end of subduction of the Magdalena plate.