Thanks for the question. With iOS 7, you can delete a song by doing the following:
Remove a song from iPhone. Tap Songs, swipe the song, then tap Delete. The song is deleted from iPhone, but not from your iTunes library on your Mac or PC, or from iCloud.
via page 62 of the iPhone User Guide for iOS 7
This will delete the song from local storage, but the song will still appear with a cloud symbol in the Music app, as you've noticed. To hide the iTunes in the Cloud purchases, navigate to Settings > iTunes & App Store, and disable "Show All: Music"