Do vampires literally piss blood?

When these vampires ingest blood, it spreads out from their esophagi into the crystallized cells in their bodies, which is used up and gives them energy. As far as I can tell, they don't create any waste products when they absorb their only sustenance, which is blood.

In the case of Edward, (or any male vampire in this series, for that matter), Bella and the others figured out in the book that when vampires are created, their bodies are basically frozen in the state they were when they were bitten. This is why female vampires can't have babies, because having a baby requires the body to change in cycles all the time, and that can't happen if your body is frozen in one state. They also don't have periods because all the blood that was inside the females when they were transformed, gets absorbed over the next year, and then, they stop having the monthly menstrual cycles like a human woman would.

But the men, on the other hand, are frozen in a state of producing semen (just like they were when they were human), and therefore can still keep on making it long after they are transformed.

Meyer does not explain why or how this happens, nor has she ever explained vampire body chemistry very well, but frankly, it was a story device for the last book in the series.