Click on the File Menu, select Delete File. The file in the viewer is removed from your hard drive (or other media). Be sure you want this, as the file is immediately removed.
The file is, by default, removed to Recycle Bin, but you can change this option in: Properties->File Handling.
If you delete a file by accident, just resave the image.
There is also a Delete option on the Edit Menu. This only removes the file from the viewer (memory), it doesn’t affect the file on your hard drive.