In this paper, we present a quasi-optically coupled 600-GHz high-temperature superconducting (HTS) sub-harmonic mixer for communication and sensing applications. The mixer features an innovative double-Y-type slot integrated lens antenna, which can efficiently couple the radio frequency (RF) and local oscillator (LO) signals with a small frequency ratio by exciting the half-wave and full-wave resonant current modes on the slot, respectively. Considering the low impedance characteristics of HTS Josephson junctions, a coplanar-waveguide stepped impedance transformer is utilized for minimizing the mismatching loss. A cascaded filter network is designed to prevent the high-frequency signal leakage at both bands while coupling the intermediate-frequency (IF) signal output efficiently. Based on this antenna design and an established HTS step-edge junction technology, a 600-GHz mixer prototype was designed, fabricated and measured, which was compared with the simulation results. The achieved conversion gain and noise temperature are the best performance specs as reported to date for HTS harmonic mixers at comparable frequencies and operating temperatures.