That's the cause of your problem, or at least the first thing you need to address.

If it were me, I would:

• It looks like your backup job just completed but if you could not start mysql, I am not sure if the backup is complete.
• Clean up anything you don't need. look for big files in /var/log or /tmp that are suspicious or old and remove them. 
• Once you get enough space to start mysql, run a backup again.
• Depending on how much space you can clean up, you may want to increase the filesystem size. If you created this applaince with a logical volume, you can add a disk and extend the volume giving you more space. If you did not use a logical volume it's trickier but you can either extend the partition and filesystem (if you have physical disk space unused) or deploy a new wordpress instance and use tklbam to restore your data.