If someone can't be rehabilitated, they should be contained[0]
| If they need to be contained, we have additional concerns with deportation.
| | If they are being deported freely to another country (i.e. not through extradition), then we are doing (at least) similar harm to another as to what harm would be if we just let them go in our own country. Personal ethics aside, this creates disorder and enemies. It is one thing if extradition is attempted and this is the result after failure, but it is another if the process doesn't happen. This is analogous to capturing all the rattlesnakes in my backyard and throwing them into yours. "Not my problem" isn't so accurate when I piss you off and now I have a new problem which is you being pissed at me and seeking your own form of justice. In the short term, being an asshole is an optimal strategy, but in the long term is really is not.
| | If they are being extradited to another country and that country is known to torture or do things that we do not believe are humane to their inmates, then I similarly agree we should not extradite and it is better to contain here. The blood is still on your hands, as they say.
Extradition (distinct from deportation) is the right move when it is believed the criminal will face the rule of law, fairly and in accordance to our own ethics (how we would treat our own).
I see no situation in which extra-judicial deportation (or extradition!) is the right course of action. It is also critical to recognize that mistakes happen. Even if cumbersome, the judicial process reduces the chance for mistakes. It's also worth noting that, by design, the judicial system is biased such that when mistakes occur there is a strong preference that a criminal is left unpunished rather than an innocent be prosecuted (an either or situation). We want to maximize justice, I doubt there is many who do not. But when it comes down to it, there is a binary decision at the end of the day "guilty or not guilty." We engineer failure into the judicial system just like we do in engineering. You do not design a building to fail, but you do design a building such that when it does fail, it is most likely to fail in a predictable manner which causes the least harm. And if you don't want to take my word on it, you can go consult Blackstone, John Adams, Benjamin Franklin, and many others. Because at the end of the day, I'm not the one who created this system, but I do agree with their reasoning.
[0] Not killed, because if we are wrong about the inability the rehabilitate then the cost is higher than the cost of custodianship.