How can I break external links in PowerPoint 2007?

Just updating this for Powerpoint 2010 (also works in PPT 2013). If you get this warning message "powerpoint references to external pictures have been blocked":

1. Find the offending links by File -> Info -> Edit Links To Files (in the bottom right of the Backstage view). (Also referenced in in Rhys's answer.) This will give you the name of the offending link, but annoyingly doesn't tell you which slide it is.

2. Since the PPTX file is actually a zip file:

   • copy the pptx file
   • rename the copy to have a .zip extension
   • extract the contents (e.g., right-click -> Extract all files)
   • search (e.g., using grep or Windows Explorer) through the contents of the XML files (one per slide) found at folder_where_unzip_was_done\ppt\slides, or the _rels directory below that.

   You should search for the URL (or part of it) that was revealed by the "Edit Links To Files" utility noted above. In this way you can find and fix the offending slide.

Press the Office button, then goto Prepare and selecting Edit Links to Files (you may need to scroll down the list to find it). This will bring up the dialog showing the external links, which you can then break.