MTGNexus

What happens with cards that have been mutated and then say an Unsummon is cast on it? Will both cards go back to hand?

What if I mutated Illuna, Apex of Wishes onto Arcanis the Omnipotent? If I spend 2uu will both Illuna, Apex of Wishes AND Arcanis the Omnipotent go back to hand?

What happens when they get exiled and return to play aka Cloudshift? Do they both come back as a single mutated creature? Maybe both come back individually, or maybe one doesn't come back at all?

The exact rules for the mutate mechanic haven't been released yet. However, the mechanics article for Ikoria: Lair of Behemoths says: "If a mutated creature leaves the battlefield, all of its components go to the appropriate zone." It thus follows that if Arcanis is mutated with Illuna, and Arcanis---

• is returned to its owner's hand (or otherwise goes to another zone) both Arcanis and Illuna will go to that hand (or that other zone, respectively).
• is exiled and returns to the battlefield, both Arcanis and Illuna will be exiled and return to the battlefield (and Arcanis won't be mutated), since the effect in question can find both objects since it "causes [them] to move to a public zone", namely exile (C.R. 400.7h, 400.2).

Note that only a creature spell with mutate can cause a creature to mutate; a creature with mutate that enters the battlefield can't do so. (Note that a mutating creature spell doesn't enter the battlefield when it resolves.)