Silencing "Your disk is almost full" notifications. What works?
From this Apple-recommended answer on this discussion:


  When that message appears, it should not be ignored. The only way to stop it from appearing is to increase available storage space so that your Mac can continue to work normally. 


Cache can take up a lot of space. 

To remove cache folders:


  Open a Finder window and select Go in  the menu bar.
  
  Click on “Go to Folder…”
  
  Type in ~/Library/Caches
  
  Delete the files/folders that are taking up  the most space.
  
  Now click on “Go to Folder…”
  
  Type in /Library/Caches (simply lose  the ~ symbol)
  
  And, again, delete the folders that take up the most space.


When the message appears you can also click manage and see what options optimise storage offers. This moved unused files to iCloud.

Alternatively, you can check your Mac for unused files or download a file cleaning application. 

To find out what is taking up your space go to manage storage.