Yes.. but really no
Per the spell description:
This spell repairs a single break or tear in an object you touch, such as a broken chain link, two halves of a broken key, a torn cloak, or a leaking wineskin.
Your description is a little at odds. You first describe the mirror as "broken into two" but then say "but gathering all the chips from the back of the mirror is impossible". So is the mirror in two or is it shattered?
I'm going to assume shattered. Because if it was really just two pieces, you could hold them together and see the map; no mending required.
The spell is very clear in that it can put two pieces back together, but never mentions replacing missing pieces. So you can build the puzzle one piece at a time (and with shattered glass, that could be 100+ castings). But you cannot replace what it not there to mend. Optionally, you could argue that if you put everything together it would be one casting like multiple threads being fixed at once.
So yes, the mirror COULD be fixed, if you had all the pieces, and could fit them back together the way they originally aligned. But, in your situation, no.
On top of that, as a DM I would rule you don't know what the finished product should look like so you would never build the map back to it's original design. A dress with a tear is easy to figure out. Two halves of a key you can logic out how they should touch. But you're looking at putting back together a shmuzzle; Fits together trillions of WRONG ways,
but only one RIGHT way. And someone threw away the picture of the finished picture.