There is no way to know what the most effective way to disrupt and limit this network is. We can only try things that seem to make sense and hope that they work. Let us look at a few means of disruption that seem like they could work and, perhaps, are working.
One method is to pay very close attention to how money gets to the terrorist groups. The idea would be to identify the ways in which they get their money and then to shut down those means. By doing these things, the US can limit the amount of money that gets to terrorists. This limits their ability to conduct operations.
Another thing that the US can do is try to apprehend or kill known terrorist leaders. What the US can do here is to identify terrorist leaders and try to track them as much as possible. If they can apprehend or kill those leaders, they can disrupt the terrorist organization by depriving them of their leadership. They can also cause fear in the group by making its members feel that they need to hide and cannot move freely.
Finally, we can try to persuade Muslims to think better of the United States. We can try to do things like helping people in Muslim countries. We can generally try to present ourselves as friendly to Muslims so that they do not feel as motivated to hate and attack us.
All of these are possible ways to deal with the terrorist threat.