Google Play Music

Google Play Music hosts your music in the cloud and you can stream or sync that music to your mobile device.

Music (Cache) on SD Card

By default Google Play Music caches music to your internal storage.
If you want to move the cache to an external SD card then you need to create a symbolic link to your SD Card.

Move or Clear Cache

From the information I've gathered, you need to clear the cache before moving the cache to the SD Card. But I suspect that you can just move the cache to the new location.

Create Music Directory on SD Card

Create the following folder on your SD Card:

mkdir -p /storage/sdcard1/gMusic/music

Create the Symbolic Link

Create a symlink to it in the following folder:

cd /data/data/com.google.android.music/files
ln -s /storage/sdcard1/gMusic/music

Notes

The SD Card mount point may differ on other devices. On the SGS3 its storage/sdcard1