Why A mixer is a nonlinear device that ideally produces just the sum and difference of the two input frequencies. When drive levels exceed the mixer's linear operating range, higher-order terms in its transfer characteristic come into play, so harmonics of the inputs mix as well and produce many additional unwanted output frequencies. These spurious products (often written as mF1 +/- nF2) land in the passband as birdies, intermod and images, degrading receiver dynamic range.
Watch out Terms like mixer blanking and automatic limiting are not mixer behaviors at all; limiting belongs to FM IF stages, and AGC voltage responds to detected signal level in the IF chain, not to mixer overdrive.
Overdrive a mixer and it stops being a two-tone multiplier: too much level means more products, not fewer.