$args = array(
    'date_query' => array(
        array(
            'column' => 'post_date_gmt',
            'before' => '1 year ago',
        )
    ),
    'posts_per_page' => -1,
);
$query = new WP_Query( $args );


$the_query = new WP_Query( $args );

if ( $the_query->have_posts() ) :
  while ( $the_query->have_posts() ) : $the_query->the_post();

      wp_delete_post( the_ID() );

  endwhile;
endif;

wp_reset_postdata();