There exists two conditions when you’re expected to receive the error mentioned in title of this post. Firstly, when you’re running out of space on your system hard drive and secondly, when a feature of Microsoft Office is causing this issue. In the latter case, where the problem is not actually related to memory space, but still you’re receiving the following error message which directly indicates the low disk space condition:
Microsoft Excel cannot open or save any more documents because there is not enough available memory or disk space.
To make more memory available, close workbooks or programs you no longer need.
To free disk space, delete files you no longer need from the disk you are saving to.

We faced this problem with a Excel spreadsheet downloaded from Google Docs. The spreadsheet size was less than 1MB and we have GBs of free space on the disk where this spreadsheet was saved. Also we’ve another spreadsheets saved on same location and created by Excel on local computer, which we can open without this error. So this clearly shows that this is not a memory related issue at all, plus the problem persists with spreadsheets downloaded from the Internet only.
Read : How to prevent Internet usage in Office 2013?
After a bit of research on this, we summarize that the Protected View feature of Office 2013 / Excel 2013 is root cause in generating the hiccup, so here is how to fix it:
FIX : Microsoft Excel Cannot Open Or Save Any More Documents Because There Is Not Enough Available Memory Or Disk Space
1. Open any new document in Excel, and click FILE -> Options.

2. Next, in the left pane of Excel Options window shown below, select Trust Center. Now in corresponding right pane click on Trust Center Settings button:

3. Moving on, in the Trust Center settings window, select Protected View from the left pane. Finally, uncheck/disable all options in right pane there, which are:
- Enable Protected View for files originating from the Internet
- Enable Protected View for files located in potentially unsafe locations
- Enable Protected View for Outlook attachments

Click OK, OK and then restart your system. After rebooting the machine, try to open the spreadsheet with which you’re getting error, you’ll find that this time it opens as expected.
That’s it! Checkout how to make files password protected in Office 2013.