It's a catch-22. Word loses the ability to save, and then attempts to write over the file that is currently open. But it can't write the file that is currently open because it is open and can't be overwritten while it is open.
The solution is to cancel, then use File > Save As, and rename the file. Save the renamed file and quit Word. Actually, I would restart my computer. Then, in Finder, rename the original file something else (just in case the new save isn't good) and then
rename the fresh file to the original file name. Open it, and if it is OK then delete the file that would not allow itself to be overwritten.
This could be a problem with Word, but it seems more likely to be a problem with Mac OS. You didn't tell us your update levels of either Mac OS or Office, so the next thing to do is to update both.
Make sure your Mac has a working internet connection, then:
Update Mac OS X. Open the App store and click on the Updates button. Install the updates.
After, in any Office application go to the Help menu and choose Check for Updates to launch the AutoUpdate app.
Let AutoUpdate install updates and then restart your Mac.