The following will list the categories of the current post type.
ID, 'post-type-taxonomy');
foreach ( $terms as $term ) {
echo $term->slug.' ';
}
?>
If you want to exclude one of the categories so it does not show add this:
ID, 'post-type-taxonomy');
$terms = wp_list_filter($terms, array('slug'=>'category-slug'),'NOT');
foreach ( $terms as $term ) {
echo $term->slug.' ';
}
?>