I have two vanity lights currently, and with my bathroom remodel I am installing a single over mirror vanity light. This leaves me with one unnecessary wire. How should I handle this. Simply cap it and leave it in the wall. That seems odd to me. Is there a way for this to be handles properly?

Yes, the easiest thing to do is disconnect the fixture, cap off the wires, and screw a blank plate to the box. Please note: it is illegal to spackle over the now unused electrical box - you can paint to match the walls, and/or hang a mirrror of picture over it to hide it from view.