Hi. Well, they sever the umbilical cord. Then you deliver the placenta (like a mini delivery which doesn't hurt) and that is that. Then the baby has a tiny piece of umbilical cord attached for a short time but it dries and falls off. good luck
By the way, I think this was a really excellent question. Thanks for asking it.
Lol I always wonders the same thing but didn't want to ask I asked my mom yesterday and Yea it's attached to the placenta I was scared they shuved it back inside me ! Haha