There's a potentially "yes and no" answer here. If you mean, did Joyce know about Buffy's death at the time, or immediately thereafter, that it happened in Season 1, then, obviously, she didn't, since she had no idea what the Slayer was, or what Buffy's duties involved. There was something at the end of Season 2 when Buffy asked Joyce about washing blood out of her clothes, and why she had never questioned it. If you mean, did she EVER find out, then, yes, she did, but not until a couple of years after the fact.