Exclude the first ‘n’ number of posts of a tag from home page?

A in your example, you have access to all the WP_Query Object query_vars (see [here])1, you could use the post__not_in query_var in your query. It takes an array of ids as a parameter. So first you query for your posts tagged ‘highlighted’.
While displaying them, you would add all their ids to an array like so

<?php
$do_not_duplicate = array(); // set befor loop variable as an array

while ( have_posts() ) : the_post();
    $do_not_duplicate[] = $post->ID; // remember ID's of 'highlighted' posts

    //display posts

endwhile;
?>

then you kick off another query like so.

<?php
// another loop without duplicates
query_posts( array(
    'post__not_in' => $do_not_duplicate
    )
);
while ( have_posts() ) : the_post();
    // display your posts without the highlighted
endwhile;
?>