参考文章：https://www.jianshu.com/p/0afef94dfc1d
实现效果：

前台代码

<template>
      <el-table @selection-change="handleSelectionChange" @sort-change="sortChange" v-loading="loading" id = "TableColumnID" element-loading-text="加载中..." :data="listData.List" highlight-current-row style="width: 100%;">
        <el-table-column type="selection" width="55"></el-table-column>
        <el-table-column width="80" prop="UserName" label="登录名" :show-overflow-tooltip="true" sortable="custom"></el-table-column>
        <el-table-column width="80" prop="byName" label="姓名" :show-overflow-tooltip="true" sortable="custom"></el-table-column>
        <el-table-column :formatter="roleType" prop="Role" label="用户权限" :show-overflow-tooltip="true" sortable="custom" width="150"></el-table-column>
        <el-table-column prop="LastActivityTime" label="更新时间" sortable="custom" width="200"></el-table-column>
        <el-table-column prop="CreateTime" label="创建时间" sortable="custom" width="200"></el-table-column>
        <el-table-column fixed="right" label="操作" align="center">
          <template slot-scope="scope">
            <el-button type="primary" size="small" @click="handleEdit(scope.row)">编辑</el-button>
            <el-button type="danger" size="small" @click="handleDelete(scope.row)">删除</el-button>
          </template>
        </el-table-column>
      </el-table>
    </template>

如果需要后端实现排序功能，需要将sortable设置为custom，同时在 Table 上监听sort-change事件，在事件回调中可以获取当前排序的字段名和排序顺序，从而向接口请求排序后的表格数据。

sort-change方法自带三个参数，分别代表意义是：
column：当前列
prop：当前列需要排序的数据
order：排序的规则（升序、降序和默认[默认就是没排序]）

JS代码：

 data() {
    return {
      loading: false,
      listData: [],
      addVisible: false,
      currentObj: { U: {}, UAccount: {} },
      queryData: {
        UserName: "",
        CustomerCode: "",
        CustomerName: "",
        role: 0,
        p_Role: "",
        prop : "",
        order : "",
        currentPage: 1,
        pageSize: 10
      },
      EUserP_Role: [],
      p_Role: {},
      ids: []
    };
  },
 methods: {
    sortChange(column,prop,order){
      if(column.prop == null || column.order == null){
        this.queryData.prop = "";
        this.queryData.order = "";
      }else{
         this.queryData.prop = column.prop;
         this.queryData.order = column.order;
      }
      this.getList();
    }，
    getList() {
      this.loading = true;
      this.$API.User.List(this.queryData).then(res => {
        this.loading = false;
        this.listData = res;
        this.currentPage = 1;
        this.prop = column.prop;
        this.order = column.order;
      });
    }

通过getList()方法把参数传递到后端，然后后端实现排序功能。