"Mend" is a rarity in spoken AE, except for particular usages such as mending nets, mending fences, and some sewing tasks. It's possible "mend" is a word that is "phasing out" more among younger generations in the US.
But wounds still mend, as do figurative injuries like broken hearts.

BUT if a relationship can be mended, that implies that it's just a little frayed, whereas, if it's broken, it needs to be fixed.

In the UK, the word "mend" is still in common use.
"Only last week, my stereo music player stopped working and had to be mended. Of course, I took it to a "repair shop".
In general, British socks are "darned" rather than "mended". This is a reference to the type of repair necessary to mend the hole.

Summary from thread at wordreference.com