Why can't I clear out a Multi-Select Picklist with a blank import?

We have been maxed out on fields used for years so we often reuse them.  I just import a cvs file with the external unique id and blank cells for the field I am reusing.  This clears out data in the fields so I can rename and reuse.  This is not working for 2 Multi-Select Picklists.  How do I clear out the data?  (I mean the data assigned to individual external unique id records, not the fields to select in general). 

Thank you!