The appearance of genera such as Megatherium, Mosasaurus, and Pterodactylus in the historical record are documented very well. Cuvier named these genera in various essays, but it was his Essay on the Theory of the Earth published in 1813 that explained, in Cuvier's own way, how these genera came to be on this planet. The work has been interpreted in many different ways, but the overall consensus is that Cuvier's essay and opinions embrace catastrophism very fondly. Catastrophism was originally, for lack of a better word, a fad in the geological sciences during the 19th century; it has since evolved in its scope but can still be connected with a Creationist slant. Catastrophes such as the Biblical deluge (Cuvier did not specifically reference the flood of Noah) were hypothesized to have caused the mass extinction of much or all of the life on Earth from time to time according to catastrophist beliefs. New animals and plants then took over the Earth; i.e. new life was created to populate the post-extinction Earth each time.
This sort of notion is in direct opposition to the ideas of a gradualist view like evolution, but the actual extent of Cuvier's embracing of popular catastrophism is not known. His works popularized the concept, but popularizing a concept and embracing the sensation (in Britain where it was most popular it was known as natural theology) after it becomes popular are two rather separate things. Catastrophism, "natural theology" is no longer referred to, is much more scientifically based now thanks to the work of scientists like Louis Alvarez. In some aspects it has become more accepted, however, the idea of catastrophism is still not popular with the majority of the scientific community. One of the positives of catastrophism that holds appeal is that long timelines either may or may not exist for faunal assemblages. This kind of characteristic fits very well into the concept of punctuated equilibrium.
Back to the point though. Cuvier began to use these views of catastrophes as mechanisms of change to investigate the stratigraphy of the Earth. In these investigations Cuvier laid the principles for the concept of biostratigraphy (with the aid of Alexandre Brongniart). That makes Cuvier the father of paleontology, biostratigraphy, catastrophism, and an extremely famous and well regarded anatomist. There is a lot more history and theory on catastrophism than presented here. If you are more interested, check out the Wikipedia and this video (the video is fairly neutral).