When her tribe was attacked by a vampire, many of them were killed. The NIW decided to stab herself so the vampire woman would be distracted by the smell and Taha Aki would be able to kill her.
Because there was not enough blood around, OK? Loads of people had just been savagely killed but the so-called cold woman had to smell HER blood so Taha Aki would defeat her, and then cry over his beloved wife's dead body! Just cutting her arm wouldn't have been enough and when you really love someone, the best thing to do is commiting suicide for him/her!
In the movie, the scene is actually hilarious as the NIW actually manages to stab herself without tearing her clothes. Magical fabric?
The NIW was never mentioned again but at least she set a
horrible good example to all Twilight females: sacrifice yourself for your loved one, even if it doesn't make sense at all.