I mean in the U.S., the rules are pretty simple. if you are a U.S. citizen (via birth or naturalization), then you cannot be deported (though certainly you can be imprisoned for committing crimes). If you are not, then you can be deported under certain circumstances. The U.S. government cannot send U.S. citizens to prisons in other countries for crimes committed here (though extradition may apply if an American citizens commit crimes in other countries).

Like this one guy that has been in the news a lot lately for some reason that was deported to El Salvador (where he is a citizen). He was in this country illegally, has been determined to be a member of the gang MS-13, and has a known violent history (his wife has had two restraining orders against him for instance). Deporting him is clearly the right thing to do. He has had his due process (has been in front of an immigration judge and had an appeal). There is nothing nefarious about deporting this guy and in fact is something that gets done all the time since long before Trump came into office. The fact that this is a story at all seems a little odd. Well, not really...such coverage is clearly politically motivated.

Now Trump, speaking specifically of the CECOT prison in El Salvador has said "I'm just saying if we had a legal right to do it, I would do it in a heartbeat," regarding sending U.S. citizens who have been convicted of violent crimes. However, the fact is that he does not have the legal right (I mean a court would have to ultimately decide that if he tried it but it is highly unlikely).

Keep in mind also that it is not usually the Federal government prosecuting violent crimes, it's usually the state and Trump and the Federal government doesn't even have jurisdiction in those cases.

Violent crimes at the Federal level include things like terrorism, threats against federal officials or infrastructure, kidnapping across state or international lines, use of weapons of mass destruction, use of a firearm during a violent drug trafficking crime, human trafficking and other crimes that extend beyond state boundaries.

You have many rights in the U.S. but you lose many of them upon conviction of a crime. While I don't think our government should be able to send U.S. citizens to prisons outside the country, it would also be hard to sympathize with someone convicted of, for example, human trafficking as i think a firing squad would be a better sentence. In fact, the death penalty can apply at the Federal level for some of these crimes (these mostly fall under the category of "murder with aggravating circumstances" in situations that would apply at the Federal level). I would rather see violent criminals imprisoned outside the country than not imprisoned at all though neither extreme should be necessary. "Exile" is less of an erasure than execution and I'm not sure that both can't be "justice" under the right circumstances. We aren't talking about transporting prisoners to Van Diemen's land for stealing a loaf of bread, we are talking about ways to protect society from rapists, murderers, and others that would commit violent assault.