直接上代码：

重点是：
给<el-table>加上不同的标识来利用table :key="tab === '1' ? 'tab1' : 'tab2'"

      <div class="tabs">
        <el-tabs
          v-model="processingCompleted"
          type="card"
          @tab-click="handleClick"
        >
          <el-tab-pane
            v-for="(item, index) in processingCompletedTabs"
            :key="index"
            :label="item.title"
            :name="item.name"
          />

        </el-tabs>
      </div>
      <el-table
        ref="multipleTable"
        :key="tab === '1' ? 'tab1' : 'tab2'"
        v-loading="loadingData"
        element-loading-text="努力加载中"
        element-loading-spinner="el-icon-loading"
        :data="tableData"
        height="calc(100% - 60px)"
        border
        stripe
        :row-class-name="tableRowStyle"
        @selection-change="handleSelectionChange"
      >
        <el-table-column
          v-if="tab === '1'"
          type="selection"
          align="center"
          width="55"
        />

        <el-table-column
          v-if="tab === '2'"
          type="index"
          align="center"
          width="55"
          label="序号"
        />
        <el-table-column
          v-for="(item, index) in tableColumn"
          :key="index"
          :label="item.label"
          :width="item.width"
          :align="item.align"
          :prop="item.prop"
        />
      </el-table>