I'm not sure they feel threatened and thats why they reproduce, but yes they will sometimes sprout new polyps from the cuts. Its really hit or miss, a lot of times they will just heal themselves and keep on living like they were before. Other times they sprout new babies.
Basically just slice the mat of the Zoa, don't cut into the polyp itself, just the mat around the polyps.
I might do it later and post some pictures for you. I've found more faster growth comes with dosing Vitamin C though.