There's a difference between "kill" and "incapacitate". I'm sure void-manipulating stands such as Cream and The Hand would be able to render it incapable of combat via transportation to their dimensions. GER could also reset BIG back to Carne, as other users have mentioned. However, none of this options would "kill" BIG. The only stand off the top of my head that could possibly kill BIG is Killer Queen, which would almost instantaneously disintegrate BIG. This doesn't account for the possibility that BIG could mitigate the damage by regenerating quickly enough (or by simply absorbing the energy). (I haven't read Jojo in a while, so my knowledge might be a bit rusty. Forgive me if I've made any mistakes.)
Edit: I just remembered that D4C would also have a decent chance at taking out BIG. It's victory conditions have similar caveats to Killer Queen. As long as it's able to obliterate BIG before it can heal, it should be able to win.