Add an action button to Woocommerce my account orders that open in a new window

Use the following that will add to each specific action html tag the attribute target with a _blank value opening the link in a new window:

// Your additional action button
add_filter( 'woocommerce_my_account_my_orders_actions', 'add_my_account_my_orders_custom_action', 10, 2 );
function add_my_account_my_orders_custom_action( $actions, $order ) {
    $action_slug = 'specific_name';

    $actions[$action_slug] = array(
        'url'  => home_url('/the_action_url/'),
        'name' => 'The Button Text',
    );
    return $actions;
}

// Jquery script
add_action( 'woocommerce_after_account_orders', 'action_after_account_orders_js');
function action_after_account_orders_js() {
    $action_slug = 'specific_name';
    ?>
    <script>
    jQuery(function($){
        $('a.<?php echo $action_slug; ?>').each( function(){
            $(this).attr('target','_blank');
        })
    });
    </script>
    <?php
}

Code goes in functions.php file of your active child theme (or active theme). Tested and works.

You will have to set the same unique and explicit $action_slug variable in both functions.

To target orders complete only, add if ( $order->has_status('completed') ) { in the first function only like:

add_filter( 'woocommerce_my_account_my_orders_actions', 'add_my_account_my_orders_custom_action', 10, 2 );
function add_my_account_my_orders_custom_action( $actions, $order ) {
    if ( $order->has_status( 'completed' ) ) {
        $action_slug = 'specific_name';

        $actions[$action_slug] = array(
            'url'  => home_url('/the_action_url/'),
        'name' => 'The Button Text',
        );
    }
    return $actions;
}