We report frequency-tunable terahertz (THz) generation with a photomixer driven by an ultra-broadband tunable micro-electro-mechanical system vertical-cavity surface-emitting laser (MEMS-VCSEL) and a fixed-wavelength VCSEL, as well as a tunable MEMS-VCSEL mixed with a distributed feedback (DFB) diode. A total frequency span of 3.4 THz is covered in direct detection mode and 3.23 THz in the homodyne mode. The tuning range is solely limited by the dynamic range of the photomixers and the Schottky diode/photoconductor used in the experiment.