Vocabulary terms deleted but still visible
taxonomy_term_data is the canonical location for term data so it sounds like there might be other issues going on (a broken admin display, caching, DB corruption via orphaned parent/child term, we can only guess). 

If you want a safe way to remove taxonomy, invoke the taxonomy API functions (they are the same tools the admin interface is using) via Devel, drush eval, or some other dev tool where you can execute arbitrary PHP that uses these functions to remove your desired terms: 

For example:

$my_bad_tids = [1, 2, 3];
$terms = taxonomy_term_load_multiple($my_bad_tids);
foreach ($terms as $term) { 
  taxonomy_term_delete($term-&gt;tid);
}