I don’t disagree with the answers given but I’d add that your third phrase sounds natural and it would not be surprising to hear it used in AmE. Similar construction to “My homework isn’t finished yet.”

My mission is not over yet. My mission is not complete yet. My mission has not been completed yet.

Hello. The first two sentences are correct. For the last sentence, you need to make the following change: - My mission has not been completed yet. If you have any questions, feel free to let me know!