S. R. Faruqi:

In this verse there's no special aspect of meaning, nor is there any subtlety in the theme. But in it there's an allusion; if it is not known, then the verse seems meaningless. In earlier times, it was the practice that if anyone was to be publicly disgraced in the marketplace, or if it was desir ed to make a fool of someone and humiliate him, then a mirror was placed at his throat and he was paraded around in the streets and lanes. Hanging a mirror at his throat had the implication that if the person looked at himself in the mirror, then he would realize his condition. (Among us, the idiom garebāñ meñ muñh ḍāl kar dekhnā is a souvenir of this very custom.) [A discussion of similar usages in Persian.]

The basis of Mir's verse is this custom that I have described. And an additional pleasure is that he has called the lover 'black-faced'. With regard to the dictionary meaning this is proper, because the lover is considered to have a dark brownish complexion; and in the metaphorical meaning too it is proper, because in the idiom siyah-rū means 'ill-reputed, shamed, low'. In the first line 'city' and in the second line 'world' are also fine-- that in his own city disgrace is experienced as the most distressing, and seems to be as intense as disgrace in the whole world.

FWP:

SETS
MOTIFS == MIRROR
NAMES
TERMS == DEVICE

Although shahr and tashhīr come from different roots, they create nice sound effects, and might cause the hearer initially to think them related; they might thus be considered a case of the poetic device of 'doubt about derivation'.