Semiconductor heterostructures have enabled a great variety of applications ranging from GHz electronics to photonic quantum devices. While nonlinearities play a central role for cutting-edge functionality, they require strong field amplitudes owing to the weak light-matter coupling of electronic resonances of naturally occurring materials. Here, we ultrastrongly couple intersubband transitions of semiconductor quantum wells to the photonic mode of a metallic cavity in order to custom-tailor the population and polarization dynamics of intersubband cavity polaritons in the saturation regime. Two-dimensional THz spectroscopy reveals strong subcycle nonlinearities including six-wave mixing and a collapse of light-matter coupling within 900 fs. This collapse bleaches the absorption, at a peak intensity one order of magnitude lower than previous all-integrated approaches and well achievable by state-of-the-art QCLs, as demonstrated by a saturation of the structure under cw-excitation. We complement our data by a quantitative theory. Our results highlight a path towards passively mode-locked QCLs based on polaritonic saturable absorbers in a monolithic single-chip design.