Caerulea can be grown from cuttings--about as easily as other passis, in my experience. The key, though, is to not let the vine dry out (I'm assuming you've placed the whacked end in water to keep it hydrated).

Cut the vine into sections with 2-3 nodes on each length. The vine length you've mentioned should give you 3-6 cuttings. Rather than rehash the whole process here, I'll save everyone time by directing you to Myles Irvine's excellent site, which has a detailed section on cuttings:

Here is a link that might be useful: Passiflora cuttings

I have my best luck rooting passiflora vines in water set on a heat mat. The addition of an air stone seems to help, probably by keeping the water clean. I don't think the aeration has much to do with it. I've had less than stellar results using a potting mix, even with rooting hormones. The cuttings that have been rooted in water seem to adapt just fine when transplanted into soil. So far I've rooted citrina, Lady Margaret, vitifolia, amethystina, alata, violetta, caerulea, Lavender Lady, quadrangularis, murucuja, incarnata and triloba in water.
Karyn

What's your water like, Karyn? Soft, hard, alkalai, acidic, neutral...?

We have hard water but I don't know about the pH.
Karyn

I to have had better luck with water on these guys funny how sometimes they take and other times they dont.

Hey mboston!!
What have you done with that cutting?? Did you stick it in water ?? How is it doing?? We could use an update..
Chena

It's hanging in there, literraly in the water. I also put one in dirt, lengthwise but it seems to have died. Most likely because my puppies decided to help me by "unplanting it" and it was out of the dirt for a while.

Thanks for asking!