There are two misconceptions in your question that require clarification: 1. your use of the word Islamist is misplaced, 2. that you identify groups of criminals with Islam. In the first instance, an Islamist can be defined as a person who advocates Islamic fundamentalism and/or wishes to establish a society along with its laws within the framework of Islam according to a particular view. As to the second matter, your ascription of criminals to Islam is as unjustified as the criminals’ proclamations that they are acting in accordance to Islam.
You are also correct that the violent actions of some Muslims is at odds with the teachings of Islam. However, your questions need to be put into perspective and given the proper context. Without delving into history and politics -which are both at the very core of the matter- there are many groups that fight for different causes but use the banner of Islam to justify their actions. Saying they are fighting in the way of God gives these groups a type of legitimacy along with a bit of support from some people due to the historical tensions between Muslims and Christians (now viewed as “the West”). In reality, each group has its agenda. Whether it is politics, establishing a religious society based on their narrow view of what Islam is, survival, criminal, etc… each group wants to further its goals.
If one studies the religion of Islam, the conclusion should be that Islam’s teachings are to help the individual purify him/herself, bring out the humanistic values within one’s self and through these realign him/herself with the Divine. Each of what has been mentioned entails detailed practices that penetrate the mind and soul. As a Muslim, the individual must struggle to cleanse the inner and outer self. It is a process and progression to reunite with the Almighty.
It is clear that Islam and those who create mischief are polar opposites. In fact, many of the acts that they claim are in the way of Islam are deemed criminal acts by Islam deserving capital punishments. Neither their words nor their actions represent Islam and their politics are a result of a poisoned history that many on all sides share the guilt. Islam is above such motives and other than the divine judgments carried out by the prophets of God(1), violence is unacceptable except in self-defense.
Hope this helps.
God knows best.
(1)please,see Qs&As in our section of ‘Rasul and Nabi’ to have a clear understanding.