First of all, I would recommend using the wp_list_categories function (which supports ‘exclude’ and ‘exclude_tree’ arguments) instead of get_the_category_list.

Sometimes we do not have the option of choosing which function to use. Also, it is unfortunate that the get_the_category_list function does not provide a hook to target each category in the list. So we have to use a hacky method to remove items. The following code uses regex to parse the string (list of HTML elements separated by a separator) being returned by get_the_category_list function (using ‘the_category’ filter) and removes the appropriate categories.

I would also like to note and the code below removes the “Uncategorized” category (which is the default category and the most common offender users want to remove) and also the “Feature” category (something I was using in my own code).

/**
 * Identifies the "Uncategorized", "Feature" link
 * preg_replace_callback for bu_library_hide_uncategorized function
 * 
 * @param array $regex_parts
 * @return string 
 */
function bu_library_hide_uncategorized_callback($regex_parts) {
	if( !$regex_parts or count((array)$regex_parts) != 2)
		return $regex_parts;
	
	if ( in_array($regex_parts[1], array('Uncategorized', 'Feature')) )
		return '';
	
	return $regex_parts[0];
}

/**
 * Removes the uncategorized category from $thelist string parameter
 * 
 * Ignore wp-admin requests. Unfortunately, 'the_category' filter is used in other places with 1 argument), so we must
 * make the last 2 arguments optional (or we get PHP Warnings) and quit when the 2nd argument is not supplied
 */
function bu_library_hide_uncategorized($thelist, $separator = '', $parents = '') {
	
	// short circuit for lists that do not have uncategorized category,
	// or when this function is called from wp-admin (i.e. missing separator)
	if(is_admin() or !$separator or stripos($thelist, 'Uncategorized') === false) return $thelist;
	
	$listitems = explode($separator, $thelist);
	
	$new_listitems = array();
	foreach($listitems as $item) {
		if ($new_item = preg_replace_callback('!<\s*a[^>]*>(.*?)<\s*/a[^>]*>!im', 'bu_library_hide_uncategorized_callback', $item)) {
			$new_listitems[] = $new_item;
		}
	}
	
	$thelist = implode($separator, $new_listitems);
	return $thelist;
}
add_filter('the_category', 'bu_library_hide_uncategorized', 10, 3);