When you go to File => Options => Mail => Spelling and Autocorrect, you will notice that When correcting spelling in Outlook section is greyed out and you cannot select or unselect any of the options.
This is because of a disconnect between the new version of Outlook and the old version of Office.
I found a workaround to this issue:
Search for the file Winword.exe on your computer.
Copy the file Winword.exe and go to C:\Program Files\Microsoft\Office15\ and paste the Winword.exe file in this folder.
Restart Outlook 2013.
Go back to File => Options => Mail => Spelling and Autocorrect, you will see it is no longer greyed out and you can check and uncheck options.
