Japanese よい/いい/よろしい sometimes means "... is not necessary" or "fine without ..."
- コーヒーはいいです。 (Thank you but) I don't want coffee.
- いや、いいです。 No thanks. / I don't need it. (e.g., to a salesperson)
- その話はもういい。 That's enough!
- 言い訳はよろしい。 Don't make excuses.
Therefore, "ポイントカードはよろしいですか?" means something like "You don't want to use a point card, right?" or "Are you okay without a point card?" I believe the cashier said は, not が. ポイントカードがよろしいですか would mean "Do you rather prefer a point card (over something else)?"
When you respond to it, はい or いいです means "I'm fine without it" or "I won't use one". (If はい worked in your case, I think the cashier guessed your intention from your gesture rather than your words.) If you want to use a point card, you can say いや, あります or 使います.
カードがない is indeed very confusing because it sounds like "My card is missing!", i.e., you want to use a point card but just noticed you have lost it. Read this question for the reason. カードはない at least works, although blunt.