Untag/Remove a taxonomy term from a node
With Views Bulk Operations for Drupal 7, you can execute arbitrary PHP scripts.

In order to bulk-delete a specific taxonomy term, you can make a View that shows all content with the particular term you want to remove: Be sure to add a Relationship in the View like "Content: Taxonomy terms on node" so you can filter out content with the terms you want to keep. 

Then in the same View, you'd add a VBO field to execute an arbitrary PHP script. VBO no longer uses $node but rather $entity, so you can pass through the following script modified from Dave Parrish's answer above (where field_name_of_taxonomy_term would be the name of the Term Reference or Entity Reference field where you save the taxonomy terms on the node):

for ($i = 0; count($entity-&gt;field_name_of_taxonomy_term[$entity-&gt;language]) &gt; $i; $i++) {
    if ($entity-&gt;field_name_of_taxonomy_term[$entity-&gt;language][$i]['tid'] == 'TID to Remove') {
        unset($entity-&gt;field_name_of_taxonomy_term[$entity-&gt;language][$i]);
    break;
    }
}
node_save($entity);