JSFiddle - React, Tailwind, and code Playground

HTML

<script src="//unpkg.com/vue/dist/vue.js"></script>
<script src="//unpkg.com/element-ui@2.4.11/lib/index.js"></script>
<div id="app">
    <h1>
      Table 1
    </h1>
    <el-table
      ref="multipleTable1"
      :data="tableData1">
        <el-table-column
          type="selection"
          width="55">
        </el-table-column>
        <el-table-column
          label="Date"
          width="120">
          <template slot-scope="scope">{{ scope.row.date }}</template>
        </el-table-column>
        <el-table-column
          property="name"
          label="Name"
          width="120">
        </el-table-column>
        <el-table-column
          property="address"
          label="Address"
          show-overflow-tooltip>
        </el-table-column>
    </el-table>
    
    <h1>
      Table 2
    </h1>
    <el-table
      ref="multipleTable2"
      :data="tableData2">
        <el-table-column
          type="selection"
          width="55">
        </el-table-column>
        <el-table-column
          label="Date"
          width="120">
          <template slot-scope="scope">{{ scope.row.date }}</template>
        </el-table-column>
        <el-table-column
          property="name"
          label="Name"
          width="120">
        </el-table-column>
        <el-table-column
          property="address"
          label="Address"
          show-overflow-tooltip>
        </el-table-column>
    </el-table>
</div>

SCSS

@import url("//unpkg.com/element-ui@2.4.11/lib/theme-chalk/index.css");

Babel + JSX

var Main = {
    data() {
      return {
        tableData1: [{
          date: '2016-05-03',
          name: 'Tom',
          address: 'No. 189, Grove St, Los Angeles'
        }, {
          date: '2016-05-02',
          name: 'Tom',
          address: 'No. 189, Grove St, Los Angeles'
        }, {
          date: '2016-05-04',
          name: 'Tom',
          address: 'No. 189, Grove St, Los Angeles'
        }],
        tableData2: [{
          date: '2016-05-03',
          name: 'Tom 2',
          address: 'No. 189, Grove St, Los Angeles'
        }, {
          date: '2016-05-02',
          name: 'Tom 2',
          address: 'No. 189, Grove St, Los Angeles'
        }, {
          date: '2016-05-04',
          name: 'Tom 2',
          address: 'No. 189, Grove St, Los Angeles'
        }],
        multipleSelection: []
      }
    },
    
    mounted () {
    	// Only the last one works	
    	this.$refs.multipleTable1.toggleAllSelection()
      this.$refs.multipleTable2.toggleAllSelection()
    }

  }
var Ctor = Vue.extend(Main)
new Ctor().$mount('#app')