using get_the_category to get all post categories except one

Try this:

foreach((get_the_category()) as $cat) {
    if ($cat->cat_name != 'Featured') {
        echo '<li><img src="' . get_bloginfo('template_url') . '/images/cats/' . $cat->slug . '-icon.png"/>' . $cat->cat_name . '</li>';
    }
}