The idiom to save one's breath means to keep quiet, to refrain from talking, to refuse to discuss a topic. It has a connotation of annoyance, despair, and sometimes anger.
Example 1: I told her to save her breath - I didn't trust her anymore and I didn't believe her stories either.
Example 2: John's boss told him to save his breath, because the proposal was useless anyway and there was no need to explain it.
Example 3: Your father won't consent to our marriage anyway, so you might as well save your breath and forget about him.
Example 4: Save your breath, please - I already know that you lost your job today because your secretary called for you and told me what happened.