In other posts, I've written about the history and the background of their sub-sects.
We know what happened after the battle of Siffin. The Khawarij (Kharajite) started their campaign of hatred against Uthman al-Affan, Muawiyah Abu Sufyan and Imam Ali.
Yesterday, we saw Imam Ali sending his emissary (ibn Abbas) to talk some sense into these morons. The Khawarij not only refused to listen to the other side but they have also started killing and murdering innocent souls who were not political and had nothing to do with their failed arbitration at Siffin.
One of their (Khawarij) most treacherous act was the killing of the companion of the Holy Prophet Abd Allah b. Khabbab and his family.
You may find additional information about this killing on wikipedia
Ali ibn Abi Talib had already started towards Muawiyah when he received the news that they had butchered the governor of Nahrawan namely Abdullah ibn Khabbab ibn al-Aratt and his slave maid with the child in her womb, and have killed three women of Banu Tayyi and Umm Sinan as-Saydawiyyah. Ali ibn Abi Talib sent al-Harith ibn Murrah al-Abdi for investigation but he too was killed by them. When their rebellion reached this stage it was necessary to deal with them. 
I still remember reading about this killing. The details were horrific. The Khawarij cut open a pregnant woman belly. She bled to death and the infant died too.
Imam Ali was outraged with the killing. You can find many references of Imam Ali addressing the Kharajites in a very harsh tone (as below)
"If you insist on claiming that I have erred and gone astray, why do you [also insist] upon claiming that the ummah, in general, has gone astray, and hold them responsible for my error and declare them unbelievers on account of my sins? Your swords are at the ready, and you bring them down upon innocent heads!”
 Dakake, Maria Massi (2007). The Charismatic Community: Shi'ite Identity in Early Islam. USA: State Univ of New York Pr. p. 66. ISBN 978-0-7914-7033-6.
 The Battle of Nahrawan.
 footnote in the same book points to (Maqtal, p. 16; Ibn A'tham v. 5, pp. 47, 135; Ansab, v. 2, p. 462; †abari II: 233–34; and an abbreviated version in Yaqubi, v. 2, p. 155.)