原来的请求

    axios({
      method: "Get",
      url: "http://127.0.0.1:8912/api/Sys_User/list",
      params: {
        username: localStorage.getItem("username"),
      },
    }).then((reslut) => {
      this._formFields.RequestDept = reslut.data.Data[0].Dept_Id;
    });

加入 this.$forceUpdate(); 强制刷新页面

    axios({
      method: "Get",
      url: "http://127.0.0.1:8912/api/Sys_User/list",
      params: {
        username: localStorage.getItem("username"),
      },
    }).then((reslut) => {
      this._formFields.RequestDept = reslut.data.Data[0].Dept_Id;
      this.$forceUpdate();
    });

成功解决