Hi Mary,
Sounds like yall have Maypop (Passiflora incarnata), and yes, it can become quite invasive. It forms tuberous roots a little thicker than a pencil--these spread laterally through the soil about 6 to 12 inches deep. The leaves die back during the winter, but the roots send up new shoots every spring (often in May, hence the name Maypop, although down here they usually pop in March or April). The name passion vine comes from the symbolism that some Christian monks saw in the flower--the numbers of anthers, stigma, petals and sepals matched some of the numbers symbolic of the passion of Christ.
The pulp that surrounds the seeds is edible and quite tastey. The fruits develop a very pleasant fragrance within a few days of dropping from the vines. The flower color varies across its native range, and there are all white forms as well. The main pest of the plant is the catepillar stage of the gulf fritillary butterfly. The catepillars are orange with black spines (dont worry they dont sting), and the butterflies are orange with black dots.
The best way to grow the Maypop is in a pot that is placed on a concrete paver (so the roots can't get out). If you need to kill it, I'd try some of the potions used for hard-to-kill weeds like poison ivy (e.g. Brush B Gone). Or you can dig up the roots (what else you gonna do in this pleasant weather we have, LOL).
The flowers in this post are some hybrids that I created between P. Incense (itself a hybrid) and P. caerulea. There are hundreds of passiflora species and probably hundreds of hybrids as well.
Here's a pic of one of my Maypops from Mississippi--this one has good form and color to the flower:
Mark
