It's probably one of the most talked about scenes, but also one of the most misunderstood. When Mugen takes off his geta, and swings at Sarah from behind, she actually only barely manages to dodge it. Unlike all of her dodges in their fights and Jin's fight previously, it is a dodge that lacks grace. Then, her weapon will reach Mugen first, both because Mugen spun around such was the force of his first swing, and also because of the length and pivot point of Sarah's cross spear. She stops it though, because she realizes that even though she will hit Mugen first, it will not stop the momentum of his swing, and they will both die, so she expresses her love for Mugen and stops the swing, dishonoring him to fulfill her desire for him to live. She dies, and most people think she let Mugen win, but the truth is that she let Mugen live. Even if she hadn't, she would have still died. He did win, but at a cost.