html:

<el-date-picker v-model="idStartDate" type="date" value-format="yyyy-MM-dd" :picker-options="startPickerOptions" @focus="startDateFocus" /> 至
<el-date-picker v-model="idLimitDate" type="date" value-format="yyyy-MM-dd" :picker-options="endPickerOptions" @focus="endDateFocus" />

data:

data(){
    return{
        idStartDate: '', // 开始日期
        idLimitDate: '', // 结束日期
        startPickerOptions: {},
        endPickerOptions: {},
    }
}

methods:

methods: {
    stringDateToTimestamp(stringDate) {
      return Date.parse(new Date(stringDate));
    },
    startDateFocus() {
      this.idLimitDate = ''
      let idLimitDate = this.idLimitDate;
      if (!idLimitDate) return;
      let that = this;
      that.startPickerOptions = {
        disabledDate(time) {
            return time.getTime() >= that.stringDateToTimestamp(idLimitDate) - 1 * 24 * 3600 * 1000;
          },
        };
    },
    endDateFocus() {
      let idStartDate = this.idStartDate;
      if (!idStartDate) return;
      let that = this;
      that.endPickerOptions = {
        disabledDate(time) {
          return time.getTime() <= that.stringDateToTimestamp(idStartDate);
        },
      };
    },
}

最终样式：