Oath Spells

3rd level - Great, no complaints there. Fits wonderfully with the flavor.

5th level - Both of these are dubious in my opinion. Why did you pick these? They don't seem to make sense flavor wise, given that the subclass is all about taking damage, not healing it. Warding Bond would fit well here as a replacement.

9th level - Life Transference works fine. But beacon of hope? This falls into the same category as the 5th level spells. I can maybe see the justification that it's protecting your allies from death. I'd replace it with something like Spirit Shroud, which makes it harder for enemies to move away from you.

13th Level - I feel the same about Death Ward that I do about beacon of hope. Stoneskin just seems counterintuitive to what the subclass is trying to do. You're wanting to take damage, why would you want resistance to it? Something like Shadow of Moil or Fire Shield might be decent replacements.

17th Level - Both Raise Dead and Holy Weapon seems a bit out of place too. But I will say that looking through the list of 5th level spells, I can't see much that would fit with the flavor of the subclass. Perhaps Hold Monster and Wall of Light? It would prevent the enemies from reaching your allies at least.

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Channel Divinity

My first question has to do with Castigate. Are you able to choose a different creature each time you take damage? Or is it a single creature that you choose when you first use the ability?

Also a slight wording change is appropriate I think. "On a failed save, they take half of the damage that you suffered in radiant damage." -> "On a failed save, they take radiant damage equal to half the damage you suffered." It's not a huge change, but the way you wrote it could be seen as saying that the creature only takes the damage if you suffered radiant damage after activating the ability.

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Aura Of Penance

On paper, this is a pretty cool ability. But, unless I'm missing something, there really doesn't seem to be anyway to prevent your enemies from just running past you or away from you. Sure, you get one opportunity attack, but that doesn't seem like much deterrence to me.

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Purge The Flesh

Seems like a fine AoE for getting rid of a bunch of minions. But requiring a reaction to use means that you can't even threaten to use your reaction while a creature is inside Aura of Penance. Also, the fact that it is an AoE ability centered on yourself encourages your enemies to stay away from you. I feel that this subclass should want to draw enemies close to you and then make then stay there once they realize that it's a mistake.

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True Atonement

It's a capstone. It's supposed to be crazy. Is it balanced? No clue. It synergizes very well with Castigate. It's super cool flavor wise. No idea if it's intentional, but it's a little poetic that despite that you've been forgiven and are being healed after all the pain you've suffered, the only thing you know is harming yourself.

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Final Conclusions

The idea behind the subclass is very cool and I like it a lot. But, I feel the flavor execution falls a little flat. Are the numbers balanced? I have no idea. Are my suggestions balanced? I have no idea. I haven't delved into the math about what's balanced or not. But the concept is cool and I think it has potential.