Photonics-aided terahertz (THz) wireless systems have been progressively developed to accommodate the forthcoming wireless communication with extremely high data rates in recent years. However, restrained by the obtainable signal-to-noise ratio (SNR) and the dimensions explored in THz photonic wireless systems, achieving data rates of Tbit/s and beyond is still challenging. In this paper, we present a multi-dimensional multiplexing Tbit/s THz-over-Fiber wireless communication system, by efficiently benefiting from the multiplexing gain in both optical wavelength and space domains. Enabled by a combined routine of an optical frequency comb, a low inter-core crosstalk (IC-XT) multi-core fiber and advanced digital signal processing, a line rate of up to 1176 Gbit/s over a wireless distance of 10 m in the 350 GHz band is experimentally demonstrated without any THz amplifiers, resulting in a net data rate of up to 1059 Gbit/s. To the best of our knowledge, this is the first time that beyond Tbit/s wireless data rate is successfully achieved in the THz region above 300 GHz, making a significant contribution to the development of THz-over-Fiber systems for the sixth generation (6G) wireless communication.