これはアカンヤツ。 returnが無い方ね (^^)

akan_cat_list.php

<?php function category_list( $atts ) {
	extract( shortcode_atts( array(
		'post_type'	=>	'post',
		'cat_name'	=>	'',
		'num'		=>	3,
		'class'		=>	'relational_lists',
		'order'		=>	'date',
	), $atts ) );

	global $post;
	$args = array(
	  'post_type'		=>	$post_type,
	  'category_name'	=>	$cat_name,
	  'numberposts'		=>	$num,
	  'order'			=>	$order,
	);
	$relational_posts = get_posts( $args );
		foreach( $relational_posts as $post ) {
		$post_date = get_the_time( 'Y年m月d日', $post->ID );
		$post_link = get_permalink( $post->ID );
		$post_title = get_the_title( $post->ID );
		echo '<li>' . $post_date . '<a href="' . $post_link . '">' . $post_title . '</a></li>';
	}

}
add_shortcode( 'cat_list', 'category_list' );