i solved the problem. I just fix this
public function deleteTestAction(Request $id)
To this :
public function deleteTestAction($id)
And finally i launch this commande
curl -i -X DELETE -d '{"test":{"field":"xxx"}}' http://localhost/tutonew/web/app_dev.php/api/test/4/delete
And i will have this Code :
HTTP/1.1 204 No Content