How to permanently delete a taxonomy

You can use the function wp_delete_term

$todelete = array('one','two','three');

foreach ( $todelete as $slug ) {
  $term = get_term_by('slug', $slug, 'post_tag');
  if ( ! is_wp_error($term) && ! empty($term) )
      wp_delete_term( $term->term_id, 'post_tag');
}