In the screen shot below I created a pie chart using Illustrator's graph function. As you can see the pie is easily editable using the direct selection tool to pull each segment away from one another:

If this is not working for you then you may need to reset your Illustrator preferences.
To do so:
For Macintosh Users: With Illustrator closed launch a Finder Window in column view and click on your home folder. With the Option Key pressed choose Library from the Finder Go Menu. Within the Library folder find the following two files and delete them: “Adobe Illustrator <Version #> Settings” (earlier versions of Illustrator might just say “Adobe Illustrator”) and “com.adobe.Illustrator.plist”. When Illustrator is next launched it will create new preference files and the program will be restored to its defaults.
After you’ve reset up the program (make sure that no document window is open) to your liking, it is a really good idea to create copies of your personalized “mint” preference files (make sure that you quit the program before copying them—that finalizes your customization) and use them in the future to replace any corrupt versions you may need to delete.
For Windows Users: Hold down Ctrl + Alt + Shift when launching Illustrator and respond affirmatively when asked if you want to reset.