Light-sheet fluorescence microscopy has greatly improved the speed and overall photostability of optically sectioning cellular and multi-cellular specimens. Similar gains have also been conferred by light-sheet Raman imaging; these schemes, however, rely on diffraction limited Gaussian beams that hinder the uniformity and size of the imaging field-of-view, and, as such, the resulting throughput rates. Here, we demonstrate that a digitally scanned Airy beam increases the Raman imaging throughput rates by more than an order of magnitude than conventional diffraction-limited beams. Overall, this, spectrometer-less, approach enabled 3D imaging of microparticles with high contrast and 1 µm axial resolution at 300 msec integration times per plane and orders of magnitude lower irradiation density than coherent Raman imaging schemes. We detail the apparatus and its performance, as well as its compatibility with fluorescence light-sheet and quantitative-phase imaging towards rapid and low phototoxicity multimodal imaging.