Can't cut through his neck if he has an adamantium skeleton, only the cartilage & that's if you are lucky enough to hit cartilage. Decapitation
Decapitating Wolverine would be a direct way in killing him but due to the fact that the adamantium that is laced around his body would prevent him healing, however this end is a high improbability. It is unknown however what would occur if Wolverine were to be decapitated and his head would be reattached to his body.
Drowning doesn't make sense if he has been incinerated & came back but.
Drowning would kill him but like everything else wouldn't be permanent.