Well, you have to go through the project and remove references to them. So, if a particular map plays an audio file, and you delete that audio file, then you need to go to the map and remove the reference to that audio file. Otherwise it searches for it in the folder and, when it fails to find it, it will throw that error. However, you will need to remove references to it whether you delete it straight from the folder or from the resource manager.
If you're having trouble with that, I think Blizzard wrote some kind of resource finding program which will go through a project and pinpoint where any particular graphics or audio files are used. That might be an option for you.