Hey Kevans Stephens,
Thanks for the question. If I understand correctly, it sounds like you are using iTunes Match annd when you delete songs from the iPhone and it then has an iCloud icon on it. I would recommend that you read these articles, they may be helpful in troubleshooting your issue.
iTunes Match on iPhone, iPad, or iPod touch - Apple Support
If you'd like to download the song or playlist to your iOS device, tap the download icon to the right of the song or at the bottom of the playlist.
You can delete a song or album from your iPhone, iPad, or iPod touch at any time. Don't worry; it'll still be in the cloud.
- Tap the Music app.
- Tap More > Songs at the bottom.
- Scroll or search for the song you would like to delete from your device.
- Swipe right to left on the song, and then tap Delete.
Delete songs and music videos from your iTunes library with an iTunes Match subscription - Apple Support
Thanks for using Apple Support Communities.
Have a good one,
Mario