Mutations are a variation of Magic, of which they bring out a certain property of the starter magic they stem from, resulting in a stronger form of that Magic. Information about Mutations is scarce in-game; Plasma being the first mutation players may encounter and the topic is lightly touched upon during Theos' story at Sunrise Ravine.
Contrary to what some may think, Mutations are not a combination of the First and Second Minds, instead they are both completely independent when Mutating.
The First, Second, and Third Minds will be able to mutate. If the player wishes so, they may choose to not Mutate their Magic to learn additional moves for their Source Magic.
Verdies, Angry Pirate Captain - Plasma Magic
Theos, The War Phoenix - Sun Magic and Phoenix Magic
Angel Creed - Life Magic