1.选中：

this.$refs.table.selection

2.清除：

  console.log(this.$refs.table.clearSelection());

<template>
  <div>
  <el-table
  v-if="tableData.length>0" 
    :data="tableData"
    style="width:100%"
     :height="tableHeight"
     ref="table"
     >
     <el-table-column
     type="index"
     ></el-table-column>
     <el-table-column
     type="selection"
     >
       
     </el-table-column>
    <el-table-column
      prop="date"
      label="日期"
      width="180">
    </el-table-column>
    <el-table-column
      prop="name"
      label="姓名"
      width="180">
    </el-table-column>
    <el-table-column
      prop="address"
      label="地址">
    </el-table-column>
  </el-table>
<el-button @click="clearBtn">清除</el-button>
<el-button @click="select">获取选中项</el-button>
</div>
</template>
  clearBtn(){
        console.log(this.$refs.table.clearSelection());
      },
      select(){
        console.table(this.$refs.table.selection);
      }