It could have different meanings, so it's really not clear. Is the "do you swim" a habitual question (like: "do you swim often") or does it mean "can you swim"? If it's the former, then your answer means that you do swim often. The "don't know how" could mean you don't know how you swim, it's just something that feels natural to you or it could mean you don't know how you find the time to swim often. If it's the latter, then your answer means that you can swim. In the former answer you may have used something to help you swim, but in this answer you must be able to swim completely by yourself. The "don't know how" again refers to it being natural, something you can't explain.

no, it's meaningless because in English swimming is viewed as a skill, not as a state so if you can do it -- that means you know how

In one way it does make sense. I believe you are saying that you can do something but are unaware of how you acquired the skill. This might be something an amnesiac might say. It may be easier to comprehend if you say it in reverse. Answer: I don't know how, but I do swim.

It doesn't seem to make sense! Do you mean, "I do swim but I have never learned how"?

Not really, no? Maybe something more like "Yes, I do, but I'm not very good at it?"