SOURCE

var Main = {
  data() {
    return {
      tableData: [{
        name: 'A',
        age: 20
      }, {
        name: 'B',
        age: 30
      }, {
        name: 'C',
        age: 40
      }, {
        name: 'D',
        age: 50
      }, {
        name: 'E',
        age: 60
      }]
    }
  },
  mounted() {
    const table = document.querySelector('.el-table__body-wrapper tbody')
    const self = this
    Sortable.create(table, {
      onEnd({ newIndex, oldIndex }) {
        const targetRow = self.tableData.splice(oldIndex, 1)[0]
        self.tableData.splice(newIndex, 0, targetRow)
      }
    })
  }
}
var Ctor = Vue.extend(Main)
new Ctor().$mount('#app')

<script src="//unpkg.com/sortablejs@1.7.0/Sortable.js"></script>
<script src="//unpkg.com/vue/dist/vue.js"></script>
<script src="//unpkg.com/element-ui/lib/index.js"></script>
<div id="app">
<template>
    <el-table row-key="age" border :data="tableData" style="width: 100%">
      <el-table-column prop="name" label="Name">
      </el-table-column>
      <el-table-column prop="age" label="Age">
      </el-table-column>
    </el-table>
    <pre>{{ tableData }}</pre>
  </template>
</div>

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