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Don't cut it off- she has a prolapse, as you suspected. After washing it, lube your finger (better yet, lube it with a bit of oragel (teething gel for babies) as it has some topical anesthetic in it) and GENTLY push the tissue back in. The hen will likely push it back out again, but persist and GENTLY push it back in again, keeping your finger inside her for a minute or two and GENTLY sliding it back out in order to not stimulate your hen to push the tissue back out. If it won't stay back in, you'll need to continue, over the next several days (up to 2 weeks, sometimes) to push that tissue back in. The key is keeping the tissue moist (covered in an antibiotic ointment) so it doesn't form a large scab, as the scab will impede the process (it stimulates the hen to push the tissue out again).
Make absolutely sure that the hen is separated from her flockmates and is penned by herself, as they will pick at her and possibly kill her. You don't need to stand there, poking the tissue back into your hen 24 hours a day- just a couple times a day and eventually it will stay back in. Make sure your hen is able to pass droppings, as well.
Alternatively, take her to the vet and get a purse string or modified purse string (the suture only goes part of the way around the cloaca, not all the way around) suture put in and this will keep the prolapse in until the tissue is healed. The hen may lay and egg again and the purse string suture can cause trouble, but usually the hen stops laying when she is traumatized by a prolapse. If you choose to have her stitched, ask the vet how to take the stitches out in a hurry if your hen appears to be eggbound.
hope it can help you.
