functions.php

<?php

/**
 * Exclude displayed posts from Display Posts
 * @see https://displayposts.com/2019/01/03/exclude-posts-already-displayed/
 */
function be_dps_exclude_displayed_posts( $args ) {
  global $dps_excluded_posts;
  if( ! is_array( $dps_excluded_posts ) )
      $dps_excluded_posts = [];
  $args['post__not_in'] = !empty( $args['post__not_in'] ) ? array_merge( $args['post__not_in'], $dps_excluded_posts ) : $dps_excluded_posts;
  return $args;
}
add_filter( 'display_posts_shortcode_args', 'be_dps_exclude_displayed_posts' );

/**
 * Add DPS posts to exclusion list 
 * @see https://displayposts.com/2019/01/03/exclude-posts-already-displayed/
 */
function be_dps_add_posts_to_exclusion_list( $output ) {
  global $dps_excluded_posts;
  if( ! is_array( $dps_excluded_posts ) )
      $dps_excluded_posts = [];
  $dps_excluded_posts[] = get_the_ID();
  return $output;
}
add_filter( 'display_posts_shortcode_output', 'be_dps_add_posts_to_exclusion_list' );