Islam is enormously heterogenous. To understand intraislamic violence, one needs to understand islamic history, which will provide the answer to the question. I can here merely provide a concise paragraph or two. But before, just to open us to the possibility of intraviolence, consider history of Christianity, Reformation and Thirty years war. Although the geopolitical, theological and circumstantial elements differ, is it not psychologically rather similar. Or if we draw another parallel from Confucianism, is it not similar to intrafamilial violence, and here relating to filial piety, the act of patricide. Insofar as these are the questions, are they historical, and something a historian can adequately answer?

Firstly, we have to split the Islam into subcategories, so this becomes the question of intersectarian violence. Intrasectarian, though not unheard of, was, and is, rare. The alliances were, and are, aligned.

The question is one of the primary concerns in Thomas Sizgorich´s, Violence and Belief in Late Antiquity, which I thoroughly recommend, on both early medieval Christian and Islamic militancy.

We can see the divide already during the first fitna, with Khawarij resistance against the Caliphate after the arbitration has been settled following Battle of Siffin. They differ in view to both Sunnis and Shi´a, the former accepted the leadership of the ruling, the latter that it belonged to the descendants of Ali. Khawarij were notorious for their assassinations, Ali being the victim himself.

AZARIKA, One of the main branches of the Kharidjites [q.v.]. The name is derived from that of its leader Nafic b. al-Azrak al-Hanafl al-Hanzall, who, according to al-Ashcari, was the first to cause disputes among the Kharidjites by supporting the thesis according to which all adversaries should be put to death together with their women and children (isti*rad) ...

Doctrine: The principal religious theses which separate the Azarika from the other Kharidjites are, according to al-Ashcari: 1. The exclusion from Islam (bard*a) of the quietists (al-ka*ada); 2. The examination (mihna) of all who wished to join their army; 3. Regarding as unbelievers (takfir) those Muslims who did not make the hid*ra to them; 4. The slaughter of the women and children of their adversaries (isti*rdd); 5. The exclusion from Islam (bard*a) of those who recognised takiyya either in word or deed ...

The Encyclopaedia of Islam, New Edition, Volume I: p. 810-811

But to add to that, they left Christians and Jews, and offered them shelter, and Ali, upon hearing it, wrote:

“I have taken note of what you have said about the band that passed by you and slaughtered the pious Muslim while the transgressing infidel had security with them. They are a people whom Satan has seduced.” ( Al-Tabarı , Tarı¯kh, I. 3424, trans. Hawting, The History of al-Tabarı 17, 177. )

Their contemporaries described them thusly:

As for the Khawa¯rij, they passed through the religion, and they separated themselves from the community, and they wandered away from Isla¯m, and they isolated themselves from the community and they strayed from the path, and they rebelled against the government (al-sult.a¯n); they took the sword against the umma; they made the blood of the umma permissible, as well as their possessions; they treat as an enemy anyone who disagrees with them . . . They dissociate themselves from them, and they reproach them with unbelief and enormities. They think their contentiousness in the legal prescriptions of Isla¯m is proper . . . and they say whoever tells lies or commits a few or many sins, he must die without repentance, and he is in Hell, abiding forever, deathless ...

( Ibn Abı¯ Yala¯, Tabaqa ˘ ¯t al-fuqaha¯ al-H˘ana¯bila, ed. Alı¯ Muh.ammad Umar, 1.61–62. )

That is just one instance of violence and the justifications for it. Communal violence was varied, so did the reasons for it. Principally, it was not much different than European counterparts, so here I will again recommend the above mentioned book, Thomas Sizgorich´s Violence and Belief in Late Antiquity. I do hope this is at least partially satisfactory answer, but it is one of those that goes beyond mere historical facts. One needs a book for it.

P.S. Rendering of Arabic, even not in Arabic, is abysmal.