A sub-THz (88-136 GHz) full-duplex (FD) phasedarray transceiver (TRX) integrating an RF self-interference (SI) canceller with differential feeding FD antennas is presented in this work. The LO phase generation chain controls differential transmitter outputs for the phased-array operation. The differential feeding FD antenna with differential pairs of chips achieves over 35-dB SI suppression. The SI suppression is improved by 20 dB when the SI canceller is turned on. Without any digital-domain SI cancellation (SIC), a total SI suppression of >60 dB is achieved over a 2-GHz bandwidth. The proposed neutralized mixer with over 20-dB LO feedthrough suppression and wideband RF amplifiers support a large data rate at sub-THz frequencies. This is the world's first demonstrated sub-THz FD phased-array TRX. In the over-the-air (OTA) measurements for FD mode, the proposed FD TRX achieves 6 Gb/s in 8PSK and 4 Gb/s in 16QAM. It also achieves a 112-Gb/s data rate for OTA TX-to-RX.