mysql : remove row if parent id match in primary key columan
Try this:

SELECT a.organization_id,
    a.parent_organization_id,
    a.organization_name
FROM (
    SELECT om.organization_id , 
            om.parent_organization_id, 
            om.organization_name 
    FROM `organization_master` AS om 
    LEFT JOIN organization_assigned_user AS oau ON om.organization_id = oau.organization_id 
    WHERE om.c_user_id =220 OR oau.user_id =220 
    GROUP BY om.organization_id
) a 
WHERE a.parent_organization_id NOT IN
(
    SELECT om.organization_id
    FROM `organization_master` AS om 
    LEFT JOIN organization_assigned_user AS oau ON om.organization_id = oau.organization_id 
    WHERE om.c_user_id =220 OR oau.user_id =220 
    GROUP BY om.organization_id
)
OR a.parent_organization_id IS NULL


If this works for you, consider storing results of your main SELECT (used twice in my reply) in a TEMP table and joining on that for performance purposes.