My mirror light on my car will not turn off! I have tried opening and closing it multiple times to get it to shut off and it will not! Is this going to make my battery die? Thanks!

Are you talking of the vanity mirror and its lighting in the visor?
With the key on and the visor in the downward position, the light is supposed to turn on when the mirror's cover is slid open. With the cover shut and/or the visor retracted/positioned upward then the light should turn off. If it does not turn off then the visor mirror light's switch is defective or the wirings to it is shorted and the whole visor assembly has to be changed along with a checkup of the connector/wirings.
The light should also turn off with the key off or a few seconds after the key is turned off so that the battery does not get exhausted. If not then the lamp control module may also have to be replaced.

Try pressing on the light itself.