Wordpress - How to remove _wp_http_referer from URL when using WP_List_table?

As the last commenter on that Q suggested, you should probably check for actions, remove the query args and redirect. Something like:

$doaction = $wp_list_table->current_action();
if ( $doaction && isset( $_REQUEST['SOMEVAR'] ) ) {
    // do stuff
} elseif ( ! empty( $_GET['_wp_http_referer'] ) ) {
    wp_redirect( remove_query_arg( array( '_wp_http_referer', '_wpnonce' ), stripslashes( $_SERVER['REQUEST_URI'] ) ) );
    exit;
} 

Let me help you! Overwrite the parent method display_tablenav of WP_List_Table class removing the wp_nonce_field execution.

/**
 * Generates the table navigation above or bellow the table and removes the
 * _wp_http_referrer and _wpnonce because it generates a error about URL too large
 * 
 * @param string $which 
 * @return void
 */
function display_tablenav( $which ) 
{
    ?>
    <div class="tablenav <?php echo esc_attr( $which ); ?>">

        <div class="alignleft actions">
            <?php $this->bulk_actions(); ?>
        </div>
        <?php
        $this->extra_tablenav( $which );
        $this->pagination( $which );
        ?>
        <br class="clear" />
    </div>
    <?php
}