Edit in JSFiddle

new Vue({
	el: '#app',
  data: {
      new: '',
          contacts: ['(11) 2423-2324', '(11) 4356-6567', '(31) 3976-3345']
  },
  methods: {
      handler (index, e) {
      		const contact = e.target.value
          if (!contact) {
          		console.log('removing item')
              this.contacts.splice(index, 1)
              if (this.contacts.length > 0) {
              	this.focusLastField()
              }
          } else {
          	console.log('updating item')
          	this.contacts.splice(index,1,contact)
          }
      },
      add () {
          if (this.new != '') {
              this.contacts.push(this.new)
              this.new = ''
              this.focusLastField()
          }
      },
      focusLastField () {
          const lastIndex = this.contacts.length - 1
          const selector = `[data-index="${lastIndex}"]`
          Vue.nextTick(() => {
              const field = document.querySelector(selector)
              if (field != null) {
                  field.focus()
              }
          })
      },
  }
})

<div id="app">
  <pre>{{ $data | json }}</pre>
  <div v-for="contact in contacts" track-by="$index">
      <input :data-index="$index" type="text" :value="contact" @input="handler($index, $event)">
  </div>
  <div>
      <input type="text" v-el:input-new v-model="new" @input="add" placeholder="Add a number">
  </div>
</div>