You can remove all files from an Arduino project in visual studio but if they still exist on the disk they will be re-added the next time you open the project. This is in keeping with the way the Arduino IDE works which does not have a project file. Instead, the Arduino IDE includes all source files from within the sketch program folder.
This is an important point to keep in mind when it comes to compilation. The Visual Studio compiler disregards the Visual Studio project and works exactly the same way the Arduino IDE works.