Can a mirror be filed to "shave" off a portion to make it fit?

No, it will need to be professionally cut at a glass store.

Did you talk to whoever cut it for you to see what can be done? Maybe if the 2 side edges are polished it will be enough to fit better.

i take all my glass type issues to a glass/mirror store. they are very cheap. i am sure it would cost less than $10.

Yes, they "grind" the edges of glass. To smooth it, bevel it. You can also buy a cheap grinder on Ebay (abou $25) that does this for stained glass. Your glass shop that cut it should be able to do it. I would think for free since they cut it. :)

If it's only about 1/16" you can try using garnet sandpaper to sand the edge down. Be gentle and work slow with little pressure. Make sure you have the mirror on a real flat surface just slightly overhanging the edge.

You need special equipment to cut or grind glass. The first thing I would do is take precise measurements of the cut glass to see how close it is to the measurements you gave them. The cut may not have been accurate, but even if it is, you have nothing to loose by asking them if they can make the necessary adjustment without charging you. To do it yourself you would need a wet saw and/or a wet grinder so that the glass dust/shavings does not go in the air. You also need to wear eye protection and personally I would also wear a mask. I've never used either tool but my husband has used a wet saw to cut tile. The grinding tool is to give glass cuts a smooth edge that won't cause injury with handling. I don't know how long it would take to grind off the amount you need removed. The link below is a 'how-to' video for grinding glass. https://www.youtube.com/watch?v=J9--4HhwGLM