We demonstrate the rapid generation of micron and sub-micron aerosol droplets in a microfluidic device in which a fluid drop is exposed to surface acoustic waves as it sits atop a single-crystal lithium niobate piezoelectric substrate. Little, however, is understood about the processes by which these droplets form due to the complex hydrodynamic processes that occur across widely varying length and time scales. Through a combination of experiments, scaling theory and simple numerical modelling, we elucidate the interfacial destabilization mechanisms that lead to droplet formation. Large aerosol droplets on the length scale of the parent drop dimension are ejected through a whipping and pinch-off phenomenon, which occurs at the asymmetrically formed crest of the drop due to leakage of acoustic radiation from the substrate into the drop. Smaller micron order droplets, on the other hand, are formed due to the axisymmetric break-up of cylindrical liquid jets that are ejected as a consequence of interfacial destabilization. The 10 μm droplet dimension correlates with the jet radius and the instability wavelength, both determined from a simple scaling argument involving a viscous-capillary dominant force balance. The results are further supported by numerical solution of the evolution equation governing the interfacial profile of a sessile drop along which an acoustic pressure wave is imposed. Viscous and capillary forces dominate in the bulk of the drop, but inertia is dominant in the ejected jets and within a thin boundary layer adjacent to the substrate where surface and interfacial accelerations are large. With the specific exception of drops that spread into thin films with thicknesses on the order of the boundary layer dimension prior to atomization, the free surface of the drop is always observed to vibrate at the capillary-viscous resonance frequency despite the frequency of the surface acoustic wave being several orders of magnitude larger. This is contrary to common assumptions used in deriving subharmonic models resulting in a Mathieu equation for the capillary wave motion, which has commonly led to spurious predictions in the droplet size.