I hate the "regenerating equals cannot be hurt" stuff that started in the 80s and got out of Control in the 90s. Wolverine getting hit with enough arrows to make him look like a pincushion or him not having a Problem with Poison are bad Memories from that time. I think it was Rucka, who made the healing more "realistic" so that Logan gets hit and is down for the Count or having him drown as a legitimate danger.
He is already protected from the most obivious route to stop someone with healing powers (beheading) so they should try not to overdo it. And yes I think beheading should be one of the Things the People with healing factors should not get back from.
During Lauras run as Wolverine they did this with great effect. Hand ninja trying to drown Logan showed that this power has Limits and is different than being invulnerable. Writers tend to Forget that