Get categories related to particular category

by

You can use get_categories() to get all the sub-category of parent category.

$args = array('hide_empty'=> 0,
              'child_of'=>'id_of_blog_category/id_of_portfolio_category');

$categories = get_categories($args);
foreach ($categories as $key => $value) {
    echo '<li class="'.$value->slug.'"><a href="#" rel="'.$value->slug.'">'.$value->name.'</a></li>';
}