ODBC guide

Update custom multi-select, user, or team fields (raw JSON)

Shows how to update custom fields that hold multiple values or complex types (e.g. multi-select, user, team) using raw JSON. Supply a JSON array or object as required by the field type; to clear, set the column to null. Use SELECT * FROM Fields to find your custom field IDs.

UPDATE Issues 
SET customfield_10048='[{"value":"AAA"}, {"value":"CCC"}]' --supply raw json
WITH (IssueIdOrKey='10020')

--OR-- 

UPDATE Issues 
SET customfield_10048 =null --set to null
WITH (IssueIdOrKey='10020')