Mutants

 I was watching a one of those specials about mythical monsters (in particular, the Minotaur), and as a lot of these specials tend to do, it appealed to people's knowledge of more recent popular culture. In this case, the reference was to the X-Men, in comparing them to various animal hybrids throughout mythology--your Minotaurs, your Centaurs, your Mermaids. I sort of found it maybe a little easy, and to be honest, not completely accurate, as there's relatively few X-Men characters with animal motifs. But it is possible, one supposes, to make a sizable lineup of exclusively animal based X-Men characters. There's Wolverine, Beast, Wolfsbane, Angel, and if one were to really stretch it out, Nightcrawler and Phoenix. (The 2000 movie also really played up the animal side of the so-called Evil Mutants) In fact, this panel from an issue proposes the possibility of a lineup with most of these members. (Interestingly, one is Siryn, named after the mythical singing creature, and another, Namorita, has the wings/mermaid aspect of the mythical Siryn). But in general, X-Men characters have super-powers found among most regular superhero characters, the word "mutant" is usually just used to distinguish characters who develop those powers spontaneously with an origin story.

To be honest, I think the special name-dropped the X-Men because it's generally seen as a more serious use of mutants than the Teenage Mutant Ninja Turtles, which has always been more cartoonish and tongue-in-cheek, but who's mutant characters are overwhelmingly bipedal animals or some kind of hybrid. It's quite possible over time, oral tradition and the like would conflate the two franchises, and "mutant" would almost exclusively refer to the American equivalent to Satyrs and Centaurs, which I don't think ever had an umbrella term in various ancient mythologies. I think people might use the term "monster", but monster itself would be an umbrella term which would cover undead beings like zombies and vampires, or ostensibly less sapient beings like the Jersey Devil or Sea Serpents.

It does raise questions about how beings like the Mothman and Bigfoot, which are more naturalistic, and more overtly supernatural, respectively, fit into the taxonomy. Then again, formal classifications with folklore are a relatively recent practice. In any case, the word "Mutant"used to apply to mythological beings would be in line with a Medieval America where more contemporary, clinical terms like "President" or "District" are used for fiefdoms.