Translation:The woman does not know if he is a vegetarian.
But these aren't two clauses, one is a subordinate clause. What the woman doesn't know is if the man is a vegetarian. The woman doesn't become ignorant if the man is a vegetarian, but smart if he eats meat.
I don't know if it's still helpful but as far as I understand it after every 'head word' (verbs that are in any way connected with the head like think, see,...) there need to be a comma in this context. So every time you have a sentence with a 'head word' (I really don't know a better name for it) and there is a word like ,hvis' ,om' you know that there is a comma inbetween.
But I am not a Dane so if I am wrong please correct me.