SCP-682's powers are metatextual. He's unkillable because the story says he is nearly unkillable and no solution would be satisfying. His nickname is 'the very hard to destroy reptile' for rigour's sake. You don't have to be Grant Morrison to put this together.
The solution is to alter the narrative so that there is a means of killing him that is satisfying. Unfortunately, only full-on apocalypse scenarios or the use of SCP-682 as a jobber for an even worse threat would fill that criteria.
So unless you want to unleash something even more tiresome, like the Black Moon or the Scarlet King or the Yellow Submarine or whatever other color-coded doomsday monster you have on tap, you're just wasting jumpsuit filling doing anything at all.
The easy alternative is to simply stop trying to kill him.
Just focus on holding him in the most boring, routine ways possible, rendering him increasingly less interesting and thus reducing the time between stories focused on him and thus, the resulting breaches and disasters.
Or you can do what we did. If you aren't chicken.
Ours wasn't a rotted lizard. It was a sort of mummified horse the size of a 1996 Volkswagen Harlequin, and it was a she, but otherwise same deal. Regeneration. Vat of acid. Mass casualties. Violent opposition to the use of breath mints. Endemic to all life. Po-tay-to, po-tah-to.
We figured out the how it worked, and we speed-ran the whole concept, hurling that vile beast through a veritable plinko-fall of thousands of extermination tests and controlled rampages until there was literally nothing left to do with the 'More-Than-One-Way-to-Fail-to-Kill-a Horse'.
And we trust the populace enough to not lie to them for 'their own good'. Because its funny? Sure. Profitable? Absolutely (don't worry, shareholders!)! But never for 'their own good.'
So we turned those experiments into a 17 season reality television program hosted by Greg Kinnear and force-fed them to a sludge-hungry populace.
There were 'More-Than-One-Way-to-Fail-to-Kill-a Horse' calendars, coffee mugs, t-shirts, two different animated spin-offs running at the same time for some reason, four movies starring Chris Pratt as the voice of the horse, an ongoing sketch on Late Night with Conan O'Brien, 'More-Than-One-Way-to-Fail-to-Kill-a Horse' "acid bath" sour candy flavored yogurt in a tube, a series of increasingly inadequately playtested gameboy cartridges, a 27-issue limited series from Image comics, and adorable plush mummified murder-horse plushes with little suction cups on their red-felt hooves so they can stare balefully out the back of your station wagon at that ASSHOLE Kevin in his souped up Trans AM who does not understand the concept of a safe following distance, and you JUST want to run him off the road with the magno-lifters and recreate the scene from Lost Highway with Robert Loggia, but "you can't use the magno-lifters for revenge" because it's "against OSHA regulations" and "technically assault!"
And once the first shipment of 'More-Than-One-Way-to-Fail-to-Kill-a Horse' Funko Pops hit store shelves, the creature's cultural cache cratered so hard that it became a parody of itself so predictable it's "containment" is now a Universal Studios attraction with two failed executions and a containment breach each night, with double shows on Saturdays.
Now, it was a rocky ride getting there, especially for Utah (projections say you'll get those House seats back in two, maybe three, generations at most, don't you worry!) but we've proven that even if it isn't killable, you can, in fact, beat a dead horse.
Humbert, Outreach Liaison
Melinoë Laboratories
"Hoc non veniet ad nos mordax"