I believe the water reflections are Screen Space reflections, which means they can't be applied to mirrors, because they use the existing scene rendered on the screen to form an approximate reflection (It's a fake reflection), mirrors should reflect you and what's behind you, that means it should be taking its texture data from an entirely different camera angle that's rendering the scene again (at a lower resolution) and then projecting that texture onto the mirror's surface (I'm no graphics designer, but that's how I understand the technique)
Edit: also, that means if you apply SSR to a mirror, when you look directly at it, it'll create a weird 'endless portal' like effect.