Break out the acid glue.
I was being figurative, but your premise already changed the normal laws of the universe, so you can’t go back to being an atheist now.
The earth does not have infinite resources. The health of any species relies on a robust and consistent death rate. I would very seriously question whether halting or significantly retarding the death rate would ultimately be a wise thing to do. The world is overpopulated as it is.
As to thinking the worst of people, I was being satirical, but in all seriousness, there’s no reason to assume the best about them either.
Even if this was in a country where the death penalty was done right, I’d still support not executing him until he refuses to heal someone. Unlike most serial killers there’s actually value in keeping him alive, so my usual belief that he should be disposed of efficiently doesn’t apply. I say let him live in a cell providing healings, but the moment he hesitates, he’s dogmeat. (i.e. like the second option, but with “execute” instead of “beat”)
On the other hand, the existence of one man with supernatural powers tells us something very important: that supernatural powers are possible. This means we should keep two things in mind: that other people who aren’t serial killers might have similar powers, and that this serial killer could conceivably have other, more dangerous supernatural powers. Both of these improve the benefits of just thoroughly killing the bastard and hoping it sticks.
This! 
I oppose the Death Sentence in general, so in the end it just boils down to what do you do with him as he ages in prison? Which I think is a far less interesting question. IOW, I think your initial premise of presenting a dilemma between killing him and utilizing him is a false one.
Put him in the slammer for life, no parole. He may or may not be willing to heal victims (which ones though? That’s going to be a real hornets’ nest!)
This willingness may be influenced somewhat by the conditions of his incarceration… 
And I see no problem with that.
When he dies of old age (or cancer…? now that would be ironic!) then cut him up in ribbons 1" wide for all I care.
I voted hookers and blow on general principle, but I think Happy Lendervedder brings up a good point. The number of people this asshole can cure in the course of his “career” is going to be relatively small compared to the total number of cancer patients currently in existence, and microscopic compared to the potential number of future cancer patients. There’s a risk/reward issue here. If we let him work there’s a guarantee that he will cure a certain smallish number of patients, but if we dissect him and put a crack team of scientists on him there’s a reasonable chance that we might be able to come up with a device/concoction/gene that replicates his abilites and allow us to effectively eliminate the disease altogether. The flipside of course is that we might end up killing the golden goose and get diddly squat, but I think the difference in scope between the two good outcomes makes a very strong case for putting him under the scalpel as soon as possible.
Of course we can wait until he dies and dissect him then, but who’s to say his abilities aren’t going to run out or expire? What if he gets hit by a falling elephant? Or puts himself on fire out of spite? And how many will die of cancer in the lost time?
Mystical nature of this guys power aside, what’s the difference between him and medical science? Things are routinely cured (or mitigated thus extending lifespan) today which were a death sentence in the very near past. Are you anti medicine in general?
Kill him and never let the knowledge of his power spread to the population.
Doesn’t the OP basically describe an exaggerated version of the deal the American people had with Dick Cheney?
My take on the guy (in the OP, not specifically Dick Cheney) is that if we make some kind of deal to leave him alive and let him heal people, he will eventually (on his deathbed) reveal that he’s scammed us all along. He could really have healed an unlimited number of people effortlessly – so while we thought he was laboriously healing a few hundred over the course of decades, he was actually killing every other cancer patient on Earth at the time (through inaction) except the few he healed for appearances, thus furthering his serial-killing career to unheard-of totals. But I was raised in the Twilight Zone.
“Clone him” is a great experiment
Anyway. Several choices depend on unknown facts, and may or may not present a dilemma.
- If there weren’t any moral question about the healer (suppose it were a goose instead of a human), what would be the most medically useful approach? Probably to study as many healings as possible, and dissect the goose on death. If so, dissection is a red herring: if he’s going to die anyway, there’s no reason not to dissect him[1]. And if you want to do the best thing for science you should have him cure people directly. The choice is still between “punish him or take advantage of his ability the best way possible” Conversely, if there were a pressing medical benefit to dissecting him, well, that ties in with his already-existing punishment.
[1] Traditionally the next-of-kin would have to consent, but for such an important gain and small price, I would be happy to nationalise ownership of his remains.
- Most people, even people who do really, really evil things, would choose to help dying people, rather than NOT help dying people. Even if not, if given life-in-prison, with sufficient but bland food and exercise, they would do so in exchange for comparatively small luxurious. Only in the unlikely event that he sticks to his bargaining position is the real dilemma exposes (but suppose it is.)
OK, on to my own opinions. I don’t think life-in-prison, even being allowed to keep in good physical condition, is that much better than death, so I don’t really care which he suffers, if there’s a choice between them. (The biggest risk I’d see is that people may release or torture him later on.)
In terms of immediate cost vs immediate benefit, some amount of torture may be justified. OTOH, though it’s a difficult and painful decision, I think that that setting that precedent is NOT worth it.
Whatever you do, any news coverage at all is likely to be very painful for the victims families so should be kept to a minimum.
If it does come down to bargaining with him, I’m not sure which I’d choose 
Killing him would just make him dead without bringing any of his victims back to life. But keeping him alive in a secure facility will prevent him from killing any more people but will also save the lives of dozens of people who would otherwise die.
A related thread: Variation of Skald’s killer/healer poll
Execute him. We don’t let billionaires buy their way out of a sentence by donating all their money to charity. Why let him do what is essentially the same thing?
Sure I can. I can’t FLY. I CAN go back to being an atheist whenever I feel like it.
Or, I should say, I could. Because I didn’t stop being an atheist.* My premise, silly though it is, not not suppose that God or any gods exist–only that something happened that we could not explain. It’s explicit in the OP that the healer does not claim to be a deity or angel.
Well, so what? If he squanders his power (i.e., uses them to heal any old cancer patient, regardless of whether they could be helped by normal therapies) the healer can heal about 180 people a year. If he is more judicious in his choices, he can probably do somewhere between 12 & 52. That’s not going to change the balance of population.
Moreover, all the people the healer, um, heals are going to die of something else anyway. Death always wins, as time, entropy, and finitude are all on its side. That doesn’t mean we shouldn’t kick it in the metaphorical nads as often as possible. Moreover, deaths by cancer are often torturous, and the healer has the ability to prevent a lot of needless pain. I support that without reservation.
There’s plenty of reasons to assume the best of people, but that’s another thread. Leaving that aside, assuming that a randomly chosen cancer patient is not destined to become the next Pol Pot is hardly thinking the best of him. It’s just going with the numbers. Genocidal maniacs are extremely rare. Serial killers are less rare, but still a tiny portion of the population.
*I’m an agnostic, for one thing. Well–technical agnostic, practical atheist, fan of Thor & Athena who sometimes pretends to have conversation with Aslan.
What if fucking small children gave him his magical power to heal others? The children live through it, so it’s not like exchanging a life for a life. (Remember Mr Burns needed the blood of a young boy?)
What then, huh? Huh?
Start your own thread if you want to discuss THAT.
It’s implicit in the OP, I thought, that he doesn’t know the provenance of his power. Perhaps I should have made it explicit.
I would share the concern expressed earlier the thread that his mojo comes as a consequence of his killing, 'cept that the guy’s clearly been in prison for years and presumably hasn’t offed anybody. After all, he’s exhausted all his appeals, and that takes a while.
Then you kill him, and anyone evil enough to suggest going along with it.
I think it would be a tougher decision of the possessor of the healing powers was actually a nice, upstanding citizen - are you going to force a regular citizen to do healings whether he wants to or not? How would you justify keeping a regular citizen in a lab to do healings and be studied? (Assuming that word of his powers gets out and everyone knows about them now.)
Couldn’t you just pay him good money to do it 8 hours a day?
Edit: Of course, the REAL question is can I still dissect him?
Exactly what I was going to suggest. If he’s saving you $X million a year in cancer treatments, just give him half for a 35 minute work week and you’re still better off.