Get submitted values of webform in hook_alter function
hook_alter_form() is only invoked during form array build time, not when the form is submitted, so it's not possible (as is trying to submit a form that isn't rendered to the browser yet). If you want to handle the submitted form values for your own custom processing, add a submit handler to the form array.

function MYMODULE_form_alter(&amp;$form, &amp;$form_state, $form_id) {
   if ($form_id == 'webform_client_form_ID') {
    $form['#submit'][] = 'MYMODULE_webform_client_form_ID_submit';
  }
}

function MYMODULE_webform_client_form_ID_submit($form, &amp;$form_state) {
  // @TODO: process $form_state['values'] as needed.
}