Peel and pit the mangoes and transfer the flesh to the blender along with the lime juice. Secure the lid and puree. Add the ice. Secure the lid on the blender and start at a slow speed, gradually increasing until the fruit and ice are pureed into a smooth consistency. If the blender freezes up, or doesn't seem to be making progress, tamp down on the ice or turn off the blender and stir the mixture, then resume blending.
Serve immediately, preferably in an insulated glass.