We report on a GaAs/AlAs superlattice frequency mixer for detection of submillimeter waves. The mixer is based on the nonlinear miniband transport giving rise to domains excited under the action of a microwave field. We designed the mixer for broadband operation (300 - 600 GHz). For studying basic properties, we investigated the mixer as a harmonic mixer in 15(th) order to detect radiation at a radio frequency (RF) near 300 GHz using local oscillator (LO) radiation of a frequency near 20 GHz. We reached a noise equivalent power (NEP) of about 10 fW/Hz. We also show that the use of the superlattice mixer together with a superlattice frequency multiplier allows to realize a superlattice-based free-space transmission line for submillimeter waves.