Yep, it will come back from the roots.
That being said, I know the plant will come back in climate zone 8; I have no experience with this plant in colder climates.
If the parts that you are cutting off are still green you can propagate new plants to share. Just place the cuttings up-side-down head first into a bucket of water (I use rain water) and wait.
Eventually you will see tiny white roots forming...and probably mosquito larva so change the water frequently.
A while later the new plant will begin to show itself; it will be a lighter green color at first.
Once the new plant gets a bit larger you can trim off the long stalk and cut away the 'leaves' which should be fairly well rotted from being submerged in the water. Pot up the new plants, keep them well watered and share with your friends.