We identify a new noncatalytic growth regime for molecular beam epitaxially grown GaAs nanowires (NWs) that may provide a route toward axial heterostructures with discrete material boundaries and atomically sharp doping profiles. Upon increase of the As/Ga flux ratio, the growth mode of self-induced GaAs NWs on SiO(2)-masked Si(111) is found to exhibit a surprising discontinuous transition in morphology and aspect ratio. For effective As/Ga ratios <1, in situ reflection high-energy electron diffraction measurements reveal clear NW growth delay due to formation of liquid Ga droplets since the growth proceeds via the vapor-liquid-solid mechanism. In contrast, for effective As/Ga ratios >1 an immediate onset of NW growth is observed indicating a transition to droplet-free, facet-driven selective area growth with low vertical growth rates. Distinctly different microstructures, facet formation and either the presence or absence of Ga droplets at the apex of NWs, are further elucidated by transmission electron microscopy. The results show that the growth mode transition is caused by an abrupt change from As- to Ga-limited conditions at the (111)-oriented NW growth front, allowing precise tuning of the dominant growth mode.