I suppose this was heavy, but to answer your original question, I’ve collected all of the posts id’s in an array in the first loop, and excluded those posts from the second loop using ‘post__not_in’ which expects an array of post id’s

WP_Query post__not_in documentation

<?php
$args1 = array('category_name' => 'test-cat-1', 'order' => 'ASC');
$q1 = new WP_query($args);
if($q1->have_posts()) :
$firstPosts = array();
    while($q1->have_posts()) : $q1->the_post();
        $firstPosts[] = $post->ID; // add post id to array
        echo '<div class="item">';
        echo "<h2>" . get_the_title() . "</h2>";
        echo "</div>";
    endwhile;
endif;
/****************************************************************************/
// array of post id's collected in first loop, can now be used as value for the 'post__not_in' parameter in second loops query $args
$args2 = array('post__not_in' => $firstPosts, 'order' => 'ASC' );
$q2 = new WP_query($args2);
if($q2->have_posts()) :
    while($q2->have_posts()) : $q2->the_post();
        echo '<div class="item">';
        echo "<h2>" . get_the_title() . "</h2>";
        echo "</div>";
    endwhile;
endif;
?>