You'd test it just like any other piece of audio equipment: gain, distortion, frequency response, phase shift (and, in the case of a mixer, other important properties such as crosstalk). You'd need a scope, a low-distortion sine generator and an AC millivoltmeter.
Test procedures are covered in many texts including Tremaine's Audio Cyclopedia, Audio Measurements by Crowhurst, Audio Measurement Handbook by Metzler, and Handbook for Sound Engineers (ed: Ballou).
Sorry, there are no shortcuts if you want to do it right.