Edit in JSFiddle

  const vm = new Vue({
    el: "#app",
    data: {v: "", s: []},
    methods: {
      run: function() {
        if (this.v != "") {
          if (/\d+/.test(this.v)) {
            this.s.push(this.v)
          } else {
            const l = this.s.pop()
            const r = this.s.pop()
            this.s.push(eval(`${l}${this.v}${r}`))
          }
          this.v = ""
        }
      },
    },
  })
<div id="app">
  <div class="form-horizontal">
    <div class="form-group">
      <label class="col-md-2 control-label">入力</label>
      <div class="col-md-10">
        <input class="form-control" v-model="v" @keyup="run" />
        <ul class="list-group">
          <template v-for="e in s.slice().reverse()">
            <li class="list-group-item">
              {{e}}
            </li>
          </template>
        </ul>
      </div>
    </div>
  </div>
</div>