Are you displaying a list of terms from a taxonomy, or are you wanting to filter a list of posts by excluding any posts who have the term in question?
For the first, displaying a list of terms from a taxonomy, it is currently not possible to filter the list in any way (unless I’ve forgotten about it, which is entirely possible ?? ).
If you are displaying a list of posts and wish to exclude posts who have a specific term assigned, then this is possible via PHP, but not via the shortcode. For excluding via PHP you would recite the magic words:
the_a_z_listing( array(
'post_type' => 'your_post_type',
'tax_query' => array( array(
'taxonomy' => 'your-taxonomy', # this is a taxonomy slug
'field' => 'slug', # this says that we're using slugs in the 'terms' array below
'terms' => array( 'your-terms' ), # these are term slugs and any number of them are allowed
'operator' => 'NOT IN',
) ),
) );