Does vagina need to be cut open when giving natural birth?

Not usually: You are referring to an episiotomy. Occasionally this is still done but in most cases is not necessary.

Episiotomy: It depends on where you give birth. In some parts of the world, they do episiotomy ( surgical incision on part of perineum and bottom part of vagina) to provide a clean laceration and prevent severe tears. In the us, they dont usually do that.