No, exile can never pretend to be a "humane" substitution for the death penalty. The actual results of any attempt to do so would range from the inhumane to the outright insane.
One thing that really stands out to me is, what punishments are worthy of your death penalty? Specifically, if you think it is a humane thing to let those things happen, why the heck do you think not letting it happen in your own borders, to your own people, is not hypocrisy? Really, what's the point of marking their behavior as death-penalty-worthy if it is fine to let them continue doing it, it doesn't make sense.
If some nation is using the death penalty for truly minimally problematic things that actually would be fine elsewhere, I think exile might be kinda feasible for those minimal offenses - but the worse problem is that your originating country is deeply unjust, and it's better to fix the scale of punishments (ie, that was not supposed to be death-penalty worthy to begin with) than treat exile as a straight substitute. The actual cure for these...mismatches... in a just society is not exile, but emmigration - let people choose to leave, without fault and without fuss, from places where whatever-it-is is not welcome to places where the whatever-it-is is welcome.
The death penalty is not supposed to be for petty problems. Crimes worth the death penalty, or that a society thinks worth considering for the death penalty, are serious stuff. Offhand, I'm thinking of bloody, violating, horrifying, and fundamentally not humane crimes. And your government wishes to condone that behavior, to protect those criminals, to literally say they have a right to continue acting in that way - and your government will not even let them be treated as criminal for it? No, no I don't think that's humane. At all. Ever.
Because what is going to stop them? The people who do things you actually think are badwrongevil? Why are they not wandering off and just keep killing, torturing, raping whosoever they wish? If you put them on an island, and keep them on it - that's not exile, it's imprisonment. And they're free to prey on others on that island, some of whom are going to be more vulnerable than others - especially if you're also using exile instead of regular imprisonment and not just death-penalty stuff. So it allows considerably worse conditions than regular prisons aspire to - there aren't any rules to keep people on the island safe from inhumane treatment by each other... and if you aren't concerned about those on the island preying on others there because they "deserve" not to be protected - you might as well kill them clean, it would be kinder than the suffering humans can inflict on each other with no rules or limits! There is also a greater risk of escape (boats, rafts, bridges - humans are good at traveling), or targeting those keeping them on the island, with increased freedom and possibly cooperation among the criminals, not to mention the expense and risk of providing resources for them to survive.
True exile is even worse - it only kicks them out of their originating country, and prevents them from returning. So then they leave, and travel wherever they wish, to other unsuspecting populations, and hurt people. And wherever they land will then have to deal with them, and do the things your country won't - kill them to save others, imprison or execute them. Bonus points, you now have diplomatic incidents cropping up all over the place - from those victimized populations who want to know why your counrty didn't stop the criminal before they hurt their people, and your country wanting to know why other countries are allowing such..."inhumane"... treatment of their ex-citizens. Especially since if it's "inhumane" for them to imprison or kill, any other reaction to other countries controlling their exiled criminal's behavior by those methods would make them cynical hypocrites, outsourcing their law enforcement to other countries, which those countries will not like. Eventually, there will be war where those surrounding countries will try and make the originating country act saner.
Other answers speak quite well on the how the substitution doesn't work, all the logistical problems of where to put them and what rules, but not as much on the why of it not working, the fundamental ethical problems and the types of crime involved.