Mutagen, also known as Ooze, is a mucilaginous substance that has served as a key plot device in nearly every medium of the Teenage Mutant Ninja Turtles. Any creature that is exposed to mutagen will rapidly increase in size, strength and intelligence (sometimes). It is responsible for mutating, among others, Splinter, the four Turtles, and villains such as Tokka and Rahzar.
As opposed to being labeled T.C.R.I. (Techno Cosmic Research Institute) like in the Mirage comics, the canister in which the ooze is kept is written as "T.G.R.I." (Techno Global Research Industries), in compliance with the plot. Thus, the activity identified was "Cosmic" in the company name as opposed to "Global". In the first film, the mutagen is shown as having been the substance that mutated Donatello, Raphael, Michelangelo, Leonardo, and Splinter from ordinary animals into anthropomorphic beings.
Mutagen was a much more integral part of the second movie. A Foot Clan spy within April O'Neil's news team discovered after an interview a mutant plant near the T.G.R.I. company premises. He immediately returned to The Shredder who orders the Foot Clan to procure the cause of this mutation. Having identified T.G.R.I. as the source of the ooze, the Turtles, who were also after the origin of the mutagen, could not prevent, because of numerical inferiority, Tatsu and the Foot Clan from saving the last canister from destruction and kidnapping professor Jordan Perry.
The Shredder, now having abducted Professor Perry, forced him to create a new batch of ooze, to create new mutant warriors for him to use against the Turtles. This mutagen was used to mutate a wolf cub and a baby snapping turtle into Rahzar and Tokka, respectively (although Professor Perry was able to modify the new ooze to retard the subjects' intellectual capacities, both creatures being relatively infant-like where Splinter achieved human-level intellect fairly quickly and the turtles were only limited by their initial youth).
Perry explains to the Turtles that the ooze that mutated the Turtles and Splinter was a mistake. In Perry's words, the ooze was an "an unknown mixture of discarded chemicals was accidentally exposed to a series of radiated waves", results in the creation of the ooze which has "remarkable, but dangerous mutagenic properties." Donatello was very disappointed and upset upon learning this, as he always hoped that there would be more to their origins than an accident, but Splinter encouraged him not to judge his worth based on his origins.
The professor succeeded in creating an antidote for the ooze, which mutated Tokka and Rahzar which caused the two to revert back to their original forms.
Near the end of the film, Shredder drank some mutagen to become the Super Shredder. It is unknown what, besides his natural human form, animal species' attributes the Shredder gained during this time.
In Teenage Mutant Ninja Turtles II: The Secret of the Ooze, it was mentioned that the neutralizer is made of dimethyl chloride and must be heated to 338 Kelvin (65° Celsius or 149° Fahrenheit), which must be consumed in order to be effective; the Turtles were able to trick Tokka and Rahzar into taking the anti-mutagen by freezing it into ice cubes and hiding the cubes in doughnuts.
Unfortunately, not only did they discover them but it made them queazy, causing them to burp which is retarding the anti-mutagenic reaction. Carbon dioxide is needed to speed up the processes, and the Turtles forced them to drink from the fire extinguishers.