In Gaussian Optics, beams with a circular cross section can easily be matched by using off-axis mirrors. Since the E-field distribution of a Gaussian beam mode is entirely independent in the two directions perpendicular to its axis of propagation, it is also possible to employ the formalism for asymmetric beams. Conventional off-axis mirrors, however, are not suitable to properly match these elliptical beams. In this case, astigmatic optics are required. This paper presents a method of designing astigmatic off-axis mirrors for Gaussian beam modes starting from a conventional off-axis mirror. A numerical simulation and an application for KOSMA's 1.9 THz local oscillator for the GREAT instrument on SOFIA gives evidence supporting the theory.