No - IS (ISIS) use the death penalty usually they make a video of it and post it online somewhere or other.
Death Penalty stats worldwide
http://www.theguardian.com/news/datablog/2011/mar/29/death-penalty-countries-world
At least in America, because it's a democracy, the people can hold a debate on the issue, which is exactly what's happening in some states - either get rid of the death penalty altogether or else improve the method of execution.
http://www.huffingtonpost.com/news/death-penalty-debate/
Americans have their own democratic ways of doing stuff. What's the rush? Everyone must first be allowed to have their say this way or that. And that is going to take a very long time. The group which wants to keep the death penalty is probably far more powerful politically and so forth than those who wish to get rid of the death penalty.
Here in UK we argued about getting rid of the death penalty for generations - yet everyone has this daft idea that it was an overnight done deal when in fact it was nothing of the kind. And just like bringing slavery to an end it took generations of folk to stand up and be counted on the issue of ending the death penalty.
There are those of us, moi, who believe that every single human being can be reformed, so why not try that? Yet at the same time I despair of how the law enforcement authorities go about protecting the public from known murderers - especially those of the imported kind.
Yes, even here in UK the debate continues, even though the death penalty was abolished a long time ago. There are those who want to bring it back, but only for murder, so they say. We'll see about that.