The Mystic's role in this game largely appears to be that of a quest giver, as the only other NPC in the game that can even speak does nothing. He will give the protagonist meaningless tasks to do, and given how little there is to do in the game this is actually one of the bigger "plot points". Other activities in the game include surviving and getting off the island. The Mystic will refuse to give the player any more quests for a considerable time if they kill anything, including animals, and will be even angrier if they eat something. He appears to be very religious, constantly talking about "the creator".
SuperGreatFriend's playthrough interprets him as insanely antagonistic given it is nearly impossible to survive without killing animals, and the other men on the island are happy to kill Bully Demise. When Bully goes on a rampage against the island to kill everything on it, only the Mystic is spared, as he is invulnerable due to being the only notable NPC in the game. Bully Demise claims he knows the creator from his adventures with Jesus in The You Testament, and demonstrates several powers by cheating. The Mystic does not care, and literally sleeps through this display.
It is later confirmed during WWE 2K14 that the events of Wrecked and The You Testament were some form of purgatory, and possibly explains the Mystic's invulnerability as some form of supernatural being, similar to Andre the Giant. The Mystic comes into the land of the living to get revenge on Bully Demise for destroying his domain and killing his subjects, but also to obtain the title belt from Undertaker (Retro), which apparently has unimaginable power. While he does not personally wrestle, he summons Killerman and controls him through unexplained means, acting as his "manager". Given Killerman is made up of a horde of ghosts, it is assumed he controls Killerman through his powers over the dead.