$(function() {
  $("#sortable").sortable({
    axis: 'y',
    update: function(event, ui) {
      var data = $(this).sortable('serialize');
      $.ajax({
        data: data,
        type: 'POST',
        url: 'updatesort.php'
      });
    }
  });
});

<ul id="sortable" class="ui-sortable">
  <li id="item-1"><button class="removeli">remove</button></li>
  <li id="item-2"><button class="removeli">remove</button></li>
  <li id="item-3"><button class="removeli">remove</button></li>
  <li id="item-4"><button class="removeli">remove</button></li>
  <li id="item-5"><button class="removeli">remove</button></li>
</ul>

$("#sortable button.removeli").on("click", function () {
     $(this).parent().remove();
});

$(".removeli").click(function() {
  //
  // get <li>-id for removing it from the database
  //

  $(this).closest("li").remove();

  var data = $("#sortable").sortable('serialize');
  $.ajax({
    data: data,
    type: 'POST',
    url: 'updatesort.php'
  });
});