<script src="https://www.gxlcms.com//unpkg.com/vue/dist/vue.js"></script>
<script src="https://www.gxlcms.com//unpkg.com/element-ui@2.3.8/lib/index.js"></script>
<div id="app">
<template>
 <div class="block">
 <span class="demonstration">起始日期</span>
 <el-date-picker v-model="startDate" type="date" placeholder="選擇日期" :picker-options="pickerOptionsStart" @change="changeEnd">
 </el-date-picker>
 </div>
 
 <div class="block">
 <span class="demonstration">截止日期</span>
 <el-date-picker v-model="endDate" type="date" placeholder="選擇日期" :picker-options="pickerOptionsEnd" @change="changeStart">
 </el-date-picker>
 </div>
</template>
</div>

var Main = {
 data() {
 return {
 pickerOptionsStart: {},
 pickerOptionsEnd:{},
 startDate: '',
 endDate: '',
 };
 },
 methods:{
 changeStart (){
 this.pickerOptionsStart = Object.assign({},this.pickerOptionsStart,{
 disabledDate: (time) => {
 return time.getTime() > this.endDate
 }
 })
 },
 changeEnd (){
 this.pickerOptionsEnd = Object.assign({},this.pickerOptionsEnd,{
 disabledDate: (time) => {
 return time.getTime() < this.startDate
 }
 })
 }
 }
 };
var Ctor = Vue.extend(Main)
new Ctor().$mount('#app')

@import url("http://unpkg.com/element-ui@2.3.8/lib/theme-chalk/index.css");

.block{
 margin-top:10px;
}