You are talking about infibulation, which is also known as "Pharaonic circumcision." It's the most radical form of female genital mutilation. They not only remove the clitoris and labia minora, but most of the labia majora, which are then SEWN TOGETHER COMPLETELY, leaving only a matchstick-sized hole for blood and urine to come out. Naturally it's hard to pass urine and blood through that hole. So the answer to your question is "with great difficulty". It goes without saying that sex and childbirth are even more difficult than peeing. And yet the women in these countries are usually the staunchest advocates of the procedure.
If you Google the word "infibulation", you'll find out more about it than you ever wanted to know (including the fact that some bondage types in the West do this to themselves voluntarily through piercings and other means, which I never knew before tonight, God help me). This is one (fairly long) article I found from 1991 that seems to cover most of the phenomenon..
http://www.fgmnetwork.org/Lightfoot-klei…