The Apex Mutant seems to be a failed experiment that can be found in big Apex Labs. The Mutant Apexes are also sometimes found within Glitch-like cages or cells. Also, in certain mushroom camps, a green apex(possibly mutant) can be seen in a pod. The one pictured below is within a cell adorned with Glitch Flagpoles, Glitch Chests, and bars. Nearby is a wheelbarrow.
They may or may not attack the player or the NPCs directly, but if a player touches them it inflicts a huge amount of damage well above the average damage of enemies of the world's level. The NPCs in the Lab will not attack the Mutant Apexes.
You can't capture them with capture pods and keep them as pets so far.