There's no automatic way to do so. You'd have to use a file manager to copy the mp3 files from the directory /storage/sdcard0/Android/data/com.android.google.music/files/music over to a separate directory on your external SD card. Make sure you copy the files, because if you move them, then you might cause problems with Google Play Music, since it will think it had downloaded music before to its directory, but when it can't find the music, it might crash.
Once you've copied the files over, you could go back into Google Play Music and unpin those music files. Tapping the pin icon so that it is no longer vertical means that you're removing them from local storage; however, the files you copied to your external SD card should still remain.
The mp3 files will not have a normal filename--they're all numeric, so you may want to rename them.
Why is it so cryptic and complicated? My guess is that this is a way for Google to discourage rampant piracy of music tracks.