Transmission through seemingly opaque surfaces, so-called extraordinary transmission, provides an exciting platform for strong light–matter interaction, spectroscopy, optical trapping, and color filtering. Much of the effort has been devoted to understanding and exploiting TM extraordinary transmission, while TE anomalous extraordinary transmission has been largely omitted in the literature. This is regrettable from a practical point of view since the stronger dependence of the TE anomalous extraordinary transmission on the array’s substrate provides additional design parameters for exploitation. To provide high-performance and cost-effective applications based on TE anomalous extraordinary transmission, a complete physical insight about the underlying mechanisms of the phenomenon must be first laid down. To this end, resorting to a combined methodology including quasi-optical terahertz (THz) time-domain measurements, full-wave simulations, and method of moments analysis, subwavelength slit arrays under s-polarized illumination are studied here, filling the void in the current literature. We believe this work unequivocally reveals the leaky-wave role of the grounded-dielectric slab mode mediating in TE anomalous extraordinary transmission and provides the necessary framework to design practical high-performance THz components and systems.