Is it possible to trigger a function upon a Vue data element change?

You can use a watch, like the following example:

var vm = new Vue({
  el: '#demo',
  data: {
    firstName: 'Foo',
    lastName: 'Bar',
    fullName: 'Foo Bar'
  },
  watch: {
    firstName: function (val) {
      this.fullName = val + ' ' + this.lastName
    },
    lastName: function (val) {
      this.fullName = this.firstName + ' ' + val
    }
  }
})

About your case, here is the example about how it could be implemented.

var vm = new Vue({
  el: '#demo',
  data: {
    hash: 'Foo' 
  },
  watch: {
    hash: function (val) {
      // when the hash prop changes, this function will be fired.
      location.reload()
    } 
  }
})

I hope I understood your question right.

I think this should work

var vm = new Vue({
    el: '#root',
    data: {
      hash: null
    },
    watch: {
        hash: function (val) {
          functions_to_trigger_upon_an_element_change()
        }
    },
    methods: {
        functions_to_trigger_upon_an_element_change() {
            // You code
        }
    }
 })