Spatiotemporal optical vortex (STOV) pulses carrying purely transverse intrinsic orbital angular momentum (TOAM) are attracting increasing attention because the TOAM provides a new degree of freedom to characterize light–matter interactions. In this paper, using particle-in-cell simulations, we present spatiotemporal high-harmonic generation in the relativistic region, driven by an intense STOV beam impinging on a plasma target. It is shown that the plasma surface acts as a spatial–temporal-coupled relativistic oscillating mirror with various frequencies. The spatiotemporal features are satisfactorily transferred to the harmonics such that the TOAM scales with the harmonic order. Benefitting from the ultrahigh damage threshold of the plasma over the optical media, the intensity of the harmonics can reach the relativistic region. This study provides a new approach for generating intense spatiotemporal extreme ultraviolet vortices and investigating STOV light–matter interactions at relativistic intensities.