How do extremists justify their actions using the Qur'an and what are some of the verses they cite?
Muslim extremists cherry-pick partial verses in the Qur'an, taking them out of their specific-social-historical context. This means not considering the time, place, and specific circumstances in which these verses were revealed. Using these partial verses to justify targeting and killing innocent civilians is an act that is clearly rejected by Islamic teachings which strongly prohibit taking an innocent life.
The most commonly quoted partial verse must be understood in its context, which was the struggle of the early Muslims against the Meccans who had persecuted them and driven them out of Mecca. This persecution which began in Mecca continued after the Muslims migrated to Medina. Once they established a state and an army, the Muslims fought back for the first time.
The verse says: “Kill idolaters wherever you find them, and capture them and blockade them, and watch for them at every lookout.” (Qur'an, Chapter 9:5)
However the verse continues as follows below, a part that is usually omitted by terrorist organizations: "...But if they repent and practice prayer and give alms, then let them go their way; for God is most forgiving, most merciful. And if one of the polytheists asks you for protection, then protect him, until he hears the word of God: then deliver him to a place safe for him. That is because they are people who do not know." (Qur'an, Chapter 9:5)
Note that not only are they given a chance to repent, but also that if they ask for asylum, it must be granted.
It is also important to view this and other verses in light of the overall Qur'anic message, which emphasizes general moral imperatives such as mercy, justice, kindness, or goodness. Additionally, the Qur’an and hadith (prophetic sayings), which are the two primary sources of Islamic law, place supremacy on the sacredness of life, security, and peace, and forbid the taking of innocent life. The Qur'an has a dual nature: one that is specific (particular or transitional) to the occasion, time and place, and another that is universal and permanent in nature, dealing with principles that apply for all times and places. The specific cannot be made to apply universally, while the universal always informs the specific. Terrorists who cite Qur’anic verses to justify their actions are either quoting verses out of the context and limits in which they were revealed, or ignoring universal scholarly traditions on how to read the Qur’an and misinterpreting the verses, just as anti-abortionists, white supremacists, and certain militia groups misappropriate scripture to support their skewed interpretations. These groups are primarily political in nature and have emerged out of very specific contexts.