This is a complicated question, because both sides have been shown and told as possible over the years. Personally, I believe that he could, but the question is whether or not they COULD behead him. With his entire spin coated in adamantium, it's unlikely that he could be beheaded, even through the spinal cord, as it is likely much more protected than our own. There's also the question of whether or not his body would still be capable of healing without his mind being connected or alive (given that there was a time when nothing but a few patches of skin existed after a nuclear blast in an alternate timeline and he regrew). I guess it just depends on how you want to interpret it.
It depends on what version of Wolvie we're talking about. Sometimes his healing is incredibly strong and sometimes it's weaker. Deadpool has definitely been shown to survive beheading more than once, but his healing factor is usually portrayed as stronger than Wolvie's.
