Due to their close proximity, the Large and Small Magellanic Clouds (LMC/SMC) provide natural laboratories for understanding how galaxies form and evolve. With the goal of determining the structure and dynamical state of the SMC, we present new spectroscopic data for ∼3000 SMC red giant branch stars observed using the AAOmega spectrograph at the Anglo-Australian Telescope. We complement our data with further spectroscopic measurements from previous studies that used the same instrumental configuration as well as proper motions from the Gaia Data Release 2 catalogue. Analysing the photometric and stellar kinematic data, we find that the SMC centre of mass presents a conspicuous offset from the velocity centre of its associated H i gas, suggesting that the SMC gas is likely to be far from dynamical equilibrium. Furthermore, we find evidence that the SMC is currently undergoing tidal disruption by the LMC within 2 kpc of the centre of the SMC, and possibly all the way into the very core. This is revealed by a net outward motion of stars from the SMC centre along the direction towards the LMC and an apparent tangential anisotropy at all radii. The latter is expected if the SMC is undergoing significant tidal stripping, as we demonstrate using a suite of N-body simulations of the SMC/LMC system disrupting around the Milky Way. Our results suggest that dynamical models for the SMC that assume a steady state will need to be revisited.