The Gorgon officially enters the Discworld canon in an aside in Unseen Academicals. Also one of the dragon hunters in Guards! Guards! recounted a gorgon he knew with a terrible squint, 'she kept turning her own nose to stone'.
Via Glenda Sugarbean and a busload of anonymous passengers, we learn that Sam Vimes, despite his earlier assertion to reluctance expressed in Feet of Clay, has given in and recruited a Gorgon to the City Watch. Further details are scanty, and her name is not known, but she follows the Roundworld pattern of behaviour in that, when her sunglasses were dislodged in a high wind, several people were turned to stone under her gaze. However, Unseen University was consulted, and the Wizards (presumably meaning Ponder Stibbons) managed to reset their morphological fields back to Human again. Given that in The Light Fantastic the senior wizards are all turned to stone and it is stated that nothing can be done for them (save make a nice rockery out of the one who smashed) it is clear that being turned to stone is fatal and not reversible by magic. It is likely then that the watch gorgon can only paralyse people and the good citizens of Anhk-Morpork got a bit excited and spread the rumour 'how she'd turned them all to stone, but we got better!'. Perhaps the magic necessary for turning turned-to-stone humans back into "regular" humans was developed only later?
If the rest of the dataset for a Discworld gorgon checks against the Roundworld referent, we can expect her to be female, from Ephebe, and have a healthy head of snakes that would - very briefly, admittedly - gladden the eye of any herpetologist. Although, given an earlier remark by Terry that it's hard for a girl to go through a rigorous personal cleansing routine if the snakes in your underarms persist in ripping the deodorant can from your hand and puncturing it, it may not just be her head that has snakes...
The Compleat Discworld Atlas has the information that in the Pyrinankle mountain range marking the border between Ephebe and Ur, an occupational hazard for marble quarrymen is the singluarly unpleasant sort of fauna to be found there, of a sort that might be called "mythological" except for the fact that they're alive and well and the Petrified Gorgon you just awoke with all the noise of your quarrying is now looking at you, with an expression of grumpy displeasure on her face. As they live in caves, often to be found in exactly the sort of marble-rich mountains where you'd go to do a spot of quarrying, their reaction to their homes being destroyed just to make a decorative polished frieze in a bank or temple somewhere may be inferred. However, many Gorgons are adapting to modern life and may be seen in towns and cities, wearing thick sunglasses and tightly knotted headscarves.
In Greek mythology, the Gorgon (plural: Gorgons) (Greek: Γοργών or Γοργώ Gorgon/Gorgo) was a terrifying female creature. It derives from the Greek word gorgós, which means "dreadful". While descriptions of Gorgons vary across Greek literature, the term commonly refers to any of three sisters who had hair of living, venomous snakes, and a horrifying visage that turned those who beheld it to stone. Traditionally, while two of the Gorgons were immortal, Stheno and Euryale, their sister Medusa was not, and was slain by the mythical hero Perseus.
Gorgons were a popular image of Greek mythology, appearing in the earliest of written records of Ancient Greek religious beliefs such as those of Homer. Because of their legendary gaze, images of the Gorgons were put upon objects and buildings for protection. For the same reasons, it was a very common shield design for Greek and later Macedonian warriors. For example, an image of a Gorgon holds the primary location at the pediment of the temple at Corfu. It is the oldest stone pediment in Greece and is dated to c. 600 BC.