Well, that's a matter of who's writing, what plot-line, etc. Wolverine at one point was infamous for being able to heal instantly after a wound, no matter how severe, was taken.Cheshire the Cat said:Fire a few rounds into his eyes. Scrambles his brain. Sabretooth has a way better healing factor than Wolvy and it took him months to recover from a claw to the brain. So ya, shoot him in the eye socket then when hes down cut his head off. The bones may be adamantium but the ligaments are not.
But nonetheless, I'm gonna go with the tried and true approach of MAGNETS!