Deathstroke decapitates him.
Logan isn't getting past Slade's armour, either.
How is Slade going to cut adamantium? and yes Wolverine is getting past his armor. Normal swords have done it so adamantium claws definitely can. Anything DS throws at Logan Wolverine can take. Its not the same the other way around.
Wolverine's bones are adamantium, but the tendons, muscles and joints that connect each bone are not.
Deathstroke rips Wolverine's head off of his body -- something he's more than capable of doing.
His healing factor messed with the adamantium during the bonding process and it coated his joints to make them flexible but also nigh unbreakable, hence why characters like Hulk, Ba'al, and Dracula couldn't even dislocate a joint when they've tried pulling limbs off. So Slade isn't doing anything to his joints.