In the film, he kills Raksha in Monkey Town when she comes to rescue Mowgli. During the final battle, Mowgli uses fire in order to banish Shere Khan from his jungle. Shere Khan complies and leaves the jungle.
Basically, Shere Khan was actually going to die when Mowgli shoots him in the head with a shotgun belonging to the hunter, Buldeo, who Khan had just killed. It was cut when Disney figured it would be too scary. Shere Khan does die in the 2016 film, however.
