to cut something open, such as a package of food, means to use a knife or scissors to open it up.
So, to cut "me" open means that someone will open you up with a sharp object.
This can be used to talk about surgery:
I am going to the hospital tomorrow, the doctor is going to cut me open.
It can also be used to talk about an accident:
I was snowboarding the other day. My friend and I collided and his ski pole cut me open.