I've run a couple games in D&D 5e with mutating cultists. The party fought a bunch of cultists, and most of them had pretty pathetic stat blocks, but sometimes after the party killed one I'd change it out for a tougher monster's stat block and describe how it violently mutated.

Behind the curtain, this is pretty useful because you can always decide when an encounter needs more oomph. The players can never be sure if a weak enemy is really a weak enemy or if they'll become more powerful as a result of trauma. Just like Resident Evil. It's also a technique that's broadly applicable to any RPG system.

I lean on Resident Evil a fair bit when I'm designing games. They've got a lot to teach about dungeon design, like how to use backtracking instead of simply branching paths. I also like how puzzles aren't too clever for the average player, or how they signal that locked doors might be opened not by a key but a key item.

I'm not really familiar with RE9, but a some surface level research suggests that (mechanically speaking) mutation is just "the abilities of bad guys change mid-fight".

That seems like it is easy enough to bolt onto more-or-less any game.

You just need a variant stat-block for the enemy and something to trigger it.

D&D 5.5 has a bunch of monsters with abilities which change when they are on half hit points but you can use other triggers such as "is the target is a spell" or "the GM decides the players are having too easy a time and spends a Fear point".

The trick is to come up with mutations and associated mechanics which fit the narrative.

off the top of my head, gamma world, mutant crawl classics, Mutant (and its more modern version mutant year zero).

Mutants and masterminds depending on your definition of mutation, since its more like "superhero marvel mutants" than like "radioactive mutants"

Monte cooke games also has a 5e supplement called "arcana of the ancients" that includes mutation rules that are pretty good IMO.

I dont know if it will include it, but i am like 90% sure the upcoming mystic punks from exalted funeral is going to have something to do with mutants.

There's a system-agnostic document which is a giant table for mutations. https://www.drivethrurpg.com/en/product/198038/the-metamorphica-revised?products_id=198038

i guess you'd also want some horror along with that so:

basically all "call of cthulhu" rpgs from "achtung, cthulhu!" to delta green has strange fish people mutants.

rippers, a savage worlds setting/game/supplement/whatever they call those now, allows for experimentation with monster parts, that can be easily reflavoured as mutations or lead straight up to mutation.

I'm surprised no one has mentioned Warhammer Fantasy Roleplay....or am I misunderstanding the assignment?

I think Friend Computer knows got to handle mutants.

It’d be pretty straightforward to reflavor the Apocalypse World psychic maelstrom into a mutation.