[Vlasenko Fedor]

<script src="https://cdn.jsdelivr.net/npm/vue@2.6.14/dist/vue.js"></script>
<div id="vueRoot">
  <form ref="form">
    <input name="userName" v-model="userName">
    <a href="#" v-on:click="submit">SUBMIT</a>
  </form>
</div>
<script>
new Vue({
  el : "#vueRoot",
  data : {userName : 'Ivan'},
  methods : {
    submit : function(){
    alert (`I form: ${this.userName}`)
     // this.$refs.form.submit()
    }
  }
});
</script>

как вариант https://jsfiddle.net/vlasenkofedor/ard3yLu8/