I see this more of as understandable action than justified. I don't think killing anyone is right (I know this is a cartoon, just saying if this happened in real life) but I can understand why Mrs. Puff would try to get rid of him. Unlike other episodes, SpongeBob actually injured Mrs. Puff in a really horrifying way, Mrs. Puff lost her puffness and if she gets hurts, it'd be in a worse condition, so it makes sense to me why Mrs. Puff tried to murder him. A lot of people say it's OOC for her but I disagree. Mrs. Puff tried everything to get SB out of her life but all the time, it never worked (yeah, the show has no coninuty, just talking about her character). At times, she was nice to him because she didn't feel in danger in those moments. So in conclusing, I don't think it's right for her to kill SpongeBob but I can see why she'd act like that.
Btw, I find this so ironic that Mrs. Puff gets arrested for misunderstood or cops being harsh but this time when she was trying to commit murder, she got away with it and she got her puffness back lmao.