Thanks for writing. Hardy passionflower is known for sending out suckers that pop up some distance from the main plant. There's no way to stop the plant from doing this, unfortunately. It's just the way it likes to grow.
As far as the arbor situation goes, I can't really say what's best without seeing the vine and how entangled it is. You might find it's easiest pulling or cutting the vine off the current arbor so you can replace it with a new one. I'd suggest experimenting and seeing what seems easiest to you. Depending on the type of passionflower, you may be able to cut it back considerably so you can get it off the trellis --- passionflowers are known for their fast growth.
---Justin, Senior Garden Editor, BHG.com