We present an overview of the spectral variability of the peculiar F-type hypergiant ρ Cas, obtained from our long-term monitoring campaigns over the past 8.5 yr with four spectrographs in the northern hemisphere. Between 2000 June and September an exceptional variability phase occurred when the V brightness dimmed by about a full magnitude. The star recovered from this deep minimum by 2001 April. It is the third outburst of ρ Cas on record in the last century. We observe TiO absorption bands in high-resolution near-IR spectra obtained with the Utrecht Echelle Spectrograph during the summer of 2000. TiO formation in the outer atmosphere occurred before the deep brightness minimum. Atmospheric models reveal that the effective temperature decreases by at least 3000 K, and the TiO shell is driven supersonically with M~=5.4×10-2 Msolar yr-1. Strong episodic mass loss and TiO have also been observed during the outbursts of 1945-1947 and 1985-1986. A detailed analysis of the exceptional outburst spectra is provided, by comparing with high-resolution optical spectra of the early M-type supergiants μ Cep (Ia) and Betelgeuse (Iab). During the outburst, central emission appears above the local continuum level in the split Na D lines. A prominent optical emission line spectrum appears in variability phases of fast wind expansion. The radial velocity curves of Hα and of photospheric metal absorption lines signal a very extended and velocity-stratified dynamic atmosphere. The outburst spectra indicate the formation of a low-temperature, optically thick circumstellar gas shell of 3×10-2 Msolar during 200 days, caused by dynamic instability of the upper atmosphere of this pulsating massive supergiant near the Eddington luminosity limit. We observe that the mass-loss rate during the outburst is of the same order of magnitude as has been proposed for the outbursts of η Carinae. We present calculations that correctly predict the outburst timescale, whereby the shell ejection is driven by the release of hydrogen ionization recombination energy.