You didn't mention what kind of butterfly so I looked it up:
Passion fruit vines are a favorite host plant of the Gulf Fritillary. This beautiful butterfly's caterpillars are black and spiny and very hungry. If your plant is new and tiny you'll probably want to manually kill the caterpillars before they wipe the plant out. Once your plant gets large, you can let them dine as they please because they will generally not do significant damage. Later on you'll be rewarded with colorful orange butterflies.
It's a beautiful butterfly:
Is your passion fruit vine small? Are you sure you can't let some live and just hand pick the rest for this year? Just imagine -- what it would be like if your vines were the only sanctuary left for the last of these butterflies
*I*M* going to go find out if this butterflies come to my area of the map and see if they'll eat the only passionflower vines that can grow here -- P. incarnata.
Oh! Another idea
-- if you ground-layer your vines, you can probably get more plants started, then maybe you could plant them away from your fruit production vine and transfer the baby butterflies to their OWN vines to dine on.