$old = new Product($old_id);

$new = $old->cloneSelf();

foreach($new['properties'] as $group_data) {
    foreach($group_data['properties'] as $property_id => $property) {
        if ($property['is_my']) {
            $new->addProperty($property_id, $property['value']);
        }
    }
}

$new->insert();

$new = $old->cloneSelf();
$new['title'] = 'новый товар';
$new->insert();