Mutu Clan is a group of people who don't believe in the use of Charyeok. They instead hone their bodies to do cool supernatural martial art stuff. It happens at the time you could unlock Charyeok (7 -> 8 level gap) and instead of unlocking Charyeok, you find some of your martial art's secret scrolls or something, and learn crazy physical skills.
Non-Mutu: Use Charyeok to cause magical effects and the like, and gain a new level of power with the assistance of a god.
Mutu: No gods, only the body. Gets somewhat magical effects anyways, but only stuff that could viably be explained with science.