A hammer is good if you can make noise without raising questions.
Some people, myself included, might have a rough time telling their roomates
"ohhh ... I'm just breaking apart my caapi vine" when they're asked what the hell
all the noise is.
I personally use a hunting knife to start cutting a sliver into the vine.
After it's started about 1 inch, if that, it's fairly easy to pull it the rest of the way off with my fingers.
I'm sure some vines may vary in density but, it works for me and the vine I get.
EDIT:
Some smaller vines are able to be twisted apart.
Usually if the vine I get is < one inch in diameter, I can just twist it (with some force)
and it'll separate into multiple strands that I can break into smaller pieces by hand.