[Vuejs]-Reorder dom not binding to vue array instance?

Vue will handle the DOM updates automatically, so you simply need to change the order of the elements in the array in your operate method and the DOM will update:

operate: function () {
  this.list = ['two', 'one', 'three']; 
}

If you actually want to rearrange the list instead of completely redefining it, you’ll need to call $set() or splice() on the array (see the common beginner gotchas):

operate: function() {
  var temp = this.list[0];
  this.list.$set(0, this.list[1]);
  this.list.$set(1, temp);
}