[Mjxhnapi]

The mu'tazilah were from the opposite of the intellectual spectrum, if you want to think of it that way. There were certainly simillarities between the mu'tazilah and the qadariyyah, but not the khawaarij.

The khawaawij used their belief that a sinner was a kafir to make takfir of the rulers and attempt to overthrow them, hence their name.