Yes, YES, YES you can!! IF you use Apple's Time Machine Software, which absolutely all Mac users should be using!
Microsoft Office 2011 for Mac programs, Word, Excel, Powerpoint, etc. all have Auto-Recover (by default set to every 10 minutes), and save the Auto-Recover files to a folder that is a bit hard to find, because it's hidden way at Users > usernamehomefolder > Library > Application Support > Microsoft > Office > Office 2011 AutoRecovery. You can change the AutoRecovery folder location, and you SHOULD change it to a Dropbox (or iCloud) folder location as described here:
The problem is, if you "Don't Save" when you close a file, the file will not be saved, AND the AutoRecover file will be deleted! Auurgh!Windows users, have the option to "Keep the last autosaved version if I close without saving" as described here:
But Mac users do not have that option!
But here's the trick: Time Machine may have created a Backup of the AutoRecover file! By default, Time Machine creates a backup once per hour, although you can change the backup frequency as desrcibed here:
Understand that it is better to plan in advance by saving frequently, and using Dropbox for your AutoRecovery folder, but if you have Time Machine you are likely able to recover your AutoRecover file after clicking "Don't Save".
- "Enter Time Machine" by clicking the Time Machine icon on the menu bar
- Navigate to the last Time Machine Backup
- Navigate to the AutoRecovery folder, which by default is at Users > usernamehomefolder > Library > Application Support > Microsoft > Office > Office 2011 AutoRecovery
- "Restore" the AutoRecover file (it will ask what folder you want to restore the file to)
- Open the AutoRecover file, and re-save your recovered work.