How do I delete a purchase that is on my music that I don't want
In the Music app, find the name of the song, album, or playlist that you want to remove, and tap the More Options icon. 
  From the menu that appears, tap Delete.
  To remove the song, album, or playlists from only the device that you're currently using, select Remove Download or Remove Downloads. The item stays in your library on all of your other devices.
  If you want to remove the item from your iCloud Music Library on all of your devices, tap "Delete from My Music."
  


Straight from Apple Support.