Wash the tripe several times under running water. Cut it into julienne strips. Place the strips in a large pan and cover with cold water. Bring to a boil and add one-half teaspoon of the salt and the sugar. Cover and simmer for about three hours, until the tripe is tender. Drain.
Add the tomatoes, tomato purée, green pepper, onions, celery, garlic, remaining salt, the black pepper and cayenne to the tripe. Cover and simmer for twenty minutes.
Add the ham and mushrooms. Cover and simmer for fifteen minutes longer.