Drupal - Is it possible to replace more than one form element (wrappers) triggered by only one #ajax trigger element?

Instead of returning the HTML of the single element to update, your ajax callback can return an array of ajax commands. So it can return two ajax_command_replace to replace each element.

function ajax_example_simplest_callback(&$form, $form_state) {
  return array(
    '#type' => 'ajax',
    '#commands' => array(
      ajax_command_replace("#replace_div_1", render($form['element_to_be_replaced_1'])),
      ajax_command_replace("#replace_div_2", render($form['element_to_be_replaced_2']))
    )
  );
}

Drupal 8 alternate syntax

use Drupal\Core\Ajax\AjaxResponse;
use Drupal\Core\Ajax\ReplaceCommand;

class name extends FormBase{
   function ajax_example_simplest(array $form, FormStateInterface &$form_state) {
       $response = new AjaxResponse();
       $response->addCommand(new ReplaceCommand("#replace_div_1", ($form['element_to_be_replaced_1'])));
       $response->addCommand(new ReplaceCommand("#replace_div_2", ($form['element_to_be_replaced_2'])));
       return $response;
   }
}

One diffrence is that the render command is dropped, because AjaxResponse implements Drupal\Core\Render\AttachmentsInterface

render($form['element_to_be_replaced_1'])

Adding the render still works, but I had problems when updating a TableSelect Table that way.

Pierre Buyle's answer did not work for me. However, something like the following worked.

function ajax_example_simplest_callback(&$form, $form_state) {
    $commands = array();
    $commands[] = ajax_command_replace("#replace_div_1", render($form['element_to_be_replaced_1']));
    $commands[] = ajax_command_replace("#replace_div_2", render($form['element_to_be_replaced_2']));
    $page = array('#type' => 'ajax', '#commands' => $commands);
    ajax_deliver($page);
}

Note the call to ajax_deliver(), rather than returning the array of AJAX commands.