Sir Gawain and the Green Knight predominantly features the supernatural in the character of the Green Knight himself. The Green Knight is able to survive having his head cut off and uses magic to disguise himself as Lord Bertilak. The narrator suggests he is "half-giant," linking him to a mythical creature. Lady Bertilak gives Gawain a green girdle that allegedly protects the wearer's life from harm through supernatural means. Morgan le Fay is a sorceress who sets the plot in motion, having some control over even the Green Knight himself when she sends him to Camelot's court to propose his game.
The supernatural elements of the story are meant to make the Green Knight seem eerie and to emphasize the powers of the natural world beyond the controlled artifice of King Arthur's court. That the Green Knight's main supernatural feat is to survive death emphasizes the death and resurrection imagery around the character: the Green Chapel where he waits for Gawain resembles an open grave, and the color green is associated with nature, which itself cycles through seasons of plenty and barrenness. Ultimately, this makes the supernatural merge with natural cycles, giving nature a sense of enchantment beyond human comprehension or command.