I think people are misunderstanding the ending. Since Nagato found out that shipgirls are turned into civilians/humans after sinking then this means the real Mutsu whom she fell in love with is the human Mutsu. Not the new Mutsu who she was training. So, in the end, she chose to sink to then be with the human Mutsu. Human Mutsu seems to have gathered fragments of her previous life, which is why in the end she jumps in to save Nagato and finally reunite with her after a few months of not seeing her.
They dont die, no one dies. Nagato and Mutsu are finally together again and new Mutsu will probably end up with a new Nagato they build.
So no, not a sad ending when you think about it. lol