WP Query Exclude and Start by Menu Order Offset

You can use offset to number of post to displace or pass over. Like this.

$args = array( 
  'post_type' => 'my-post-type', 
  'posts_per_page' => 3,
  'order_by' => 'menu_order',
  'offset' => '3',
  'order' => 'ASC'
);
$loop = new WP_Query( $args );
while ( $loop->have_posts() ) : $loop->the_post();