Duplicate paragraphs from node type FOO to node type BAR
EDIT: You can now find a better explanation with the code here.
I know this is old but maybe someone comes here looking for an answer like me, this is tested on Drupal 8.
I found this issue and after looking at last patch, I implemented :
$nodeDuplicate = $node-&gt;createDuplicate();

foreach($nodeDuplicate-&gt;field_paragraphs as $field){
    $field-&gt;entity = $field-&gt;entity-&gt;createDuplicate();
}

$nodeDuplicate-&gt;save();

And I got a duplicate node with duplicated paragraphs fields. If you look at the patch you will see how to add a button to Drupal etc.
Just a note field_paragraphs is the name of my field in the content type, change it with your own.
I didn't have any problem doing it this way, maybe someone has a better way but I did not find it, also at the time of writing this there is still no ported modules for cloning nodes in Drupal 8.