Hi Molly77,
Thank you for using the Apple Support Communities! It's my understanding that you are seeking help with your Apple Music library. I'd like to assist.
When you delete a specific track from your playlist, you swipe left over the track to expose the 'Delete' option. When you do this, it should not remove the track from your Apple Music library, however. Are you noticing this behavior? And if so, is this happening with all playlists or certain ones? I would recommend updating to the latest iOS 13 version to test for this behavior as well: Update your iPhone, iPad, or iPod touch - Apple Support.
Also, quoted from: Add a song to a playlist in Apple Music without adding it to your library - Apple Support, "If you have songs in your Library that you want to move to a playlist and remove from iCloud Music Library, you first need to delete the song from your library, which will remove it from all playlists. Then, add the song back from the Apple Music catalog and add it just to a playlist."
Reach back out if you need further assistance.
Regards.