Okay, I get it now, and it is, in fact, a) a bad joke because it only sort of works if you pronounce "sauna" wrong (or if you think sauna is pronounced exactly like sana) and b) badly delivered because the punch line is separate from the joke, making it seem like an added comment, without which the joke would also work (but it doesn't). The translation what corpore sano means is completely superfluous, it doesn't contribute to the joke and thus only misleads the audience about what could be the funny part. Explaining is not what made it bad, it was bad from the start

It always does, but it at least lets the puzzled figure it out. (You might want to put that in a spoiler, though.)