When a wave is incident on a complex scattering medium, the transmitted intensity differs from the incident one due to extinction. In the absence of absorption, the extinguished power is equal to the total scattered power, a well-known conservation law termed the optical theorem. Here, we extend the case of a single incident wave to the situation of scattering and extinction by multiple incoming waves. The emerging generalized optical theorem has the exciting consequence that multiple incident waves show mutual extinction and mutual transparency, phenomena that do not exist in common forward scattering or self-extinction. Based on both exact calculations of realistic three-dimensional (3D) samples containing many (up to 104) scatterers and on approximate Fraunhofer diffraction theory we make the striking observation that the total extinction of two incident waves is greatly enhanced, called mutual extinction, or greatly reduced, mutual transparency, by up to 100% of the usual single-beam extinction. In view of the surprisingly strong mutual extinction and transparency, we propose new experiments to observe mutual extinction and transparency, namely in two-beam experiments with either elastic and absorbing scatterers, in optical wavefront shaping, in dynamic light scattering, and we discuss possible applications.