According to [this answer][1], his ligaments are in fact a weak point.  And while it doesn't show him getting cut apart...

![enter image description here][2]

...Tearing him apart is entirely possible.

Note that this image is of Ultimate Wolverine, and not the main (Earth 616) Wolverine, who may or may not have sturdier ligaments.  

  [1]: http://scifi.stackexchange.com/a/17619/20533
  [2]: https://i.sstatic.net/AyiH2.jpg