I don't think that it's likely or even possible to get them all, but for those who refuse to assimilate, for those who refuse to work, those are the people who are most likely to be radicalized and the ones most easy to be found. I would have no problem sending all of those people elsewhere, or giving them a couple of years to get their ducks in a row before getting rid of them.
The American people do not have the authority to kick out anyone from the US--only corporations, oil/mining cos., hedge funds, etc. do, because they're the only ones that own and operate the pols in power.
As for Europe, it appears that some countries are slowly becoming as plutocratic as the US.
I don't know how much "should" comes into it. It's clear these acts of violence by Muslims in Europe--and there have been many serious ones--arouse intense animosity toward them among native Europeans. Some of the local people will inevitably express that through violent attacks on Muslims, and I think it's quite possible some of these may be on a large scale--maybe something like the Kristallnacht attacks on Jews in Novermber, 1938, or even worse. As Muslims continue to commit serious violence in Europe, I don't think mass deportation or even internment is out of the question. Whether anyone looking in from the outside thinks any of these things is right won't change what happens.
It is quite conceivable that the final solution could be expulsion. I don't think so, but would none the less not be surprised.