We report the design and successful operation of an superconductor-insulator-superconductor (SIS) mixer operating near the superconducting gap of niobium. A key feature of this design is the employment of a unilateral finline taper to transform the waveguide modes to microstrip signals. This transition is easy to design since it can be rigorously modeled, and also easy to fabricate being a single-layer structure. We will show that unilateral finline mixers have important advantages at THz frequencies since they exhibit wideband operation at both radio frequency (RF) and intermediate frequency (IF), allow elegant on-chip integration of the mixer circuits and result in an extremely simple mixer block that does not require a backshort or any mechanical tuners. The mixer we describe below is fed by a multiple flare-angle smooth-walled horn which exhibits beam pattern characteristic comparable to the conventional corrugated horn and yet is much easier to fabricate.In this paper, we shall present a brief discussion of the testing of the multiple flare-angle horn and detailed description of the design and testing of the mixer, covering 100 GHz bandwidth centered at 650 GHz. In particular, we will present full electromagnetic design description of the mixer chip including the superconducting effects, and the heterodyne properties of the mixer using quantum mixing theory. Mixer performance tests that we carried out from 595 to 702 GHz gave a best receiver noise temperature of 145 K at 600 GHz, corrected for a 75 m beam splitter.Finally, we performed a thorough analysis of the mixer performance, comparing the experimental results with theoretical models. Our investigation demonstrated that unilateral finline mixers fed by a multiple flare-angle horn can yield performance comparable to conventional designs, hence are suitable for large format mixer array at THz frequencies.