<el-date-picker
  v-model="formObj.startDate"
  type="date"
  placeholder="开始时间"
  :picker-options="startPickerOptions">
</el-date-picker>

<el-date-picker
  v-model="formObj.endDate"
  type="date"
  placeholder="结束时间"
  :picker-options="endPickerOptions">
  </el-date-picker>

computed:{
    startPickerOption(){
        let _this = this
        return {
            disabledDate(time){
                if(_this.formObj.endDate){
                    return time.getTime() > new Date(_this.formObj.endDate).getTime()
                }else{
                    return false
                }
            }
        }
    },
    endPickerOption(){
        let _this = this
        return {
            disabledDate(time){
                if(_this.formObj.startDate){
                    return time.getTime() > new Date(_this.formObj.startDate).getTime()
                }else{
                    return false
                }
            }
        }
    },
}

效果图如下：