可以组合$dateToParts和$dateFromParts

年、月、日、时、分：

db.getCollection("data").aggregate([
  {"$addFields": {
     "dateVarFull": {"$dateToParts": {date: {"$toDate" : "2020-08-27T13:00:00Z"}}}
  }},
  {"$addFields": {
    "dateVarTrunc": { "$dateFromParts": {
      'year': "$dateVarFull.year",
      'month': "$dateVarFull.month",
      'day': "$dateVarFull.day"
    }}
  }}
])

结果：

{
    "dateVarFull" : {
        "year" : NumberInt(2020), 
        "month" : NumberInt(8), 
        "day" : NumberInt(27), 
        "hour" : NumberInt(13), 
        "minute" : NumberInt(0), 
        "second" : NumberInt(0), 
        "millisecond" : NumberInt(0)
    }, 
    "dateVarTrunc" : ISODate("2020-08-27T00:00:00.000+0000")
}

周trunc使用iso8601: true参数：

db.getCollection("data").aggregate([
  {"$addFields": {
    "dateVarFull": {
       "$dateToParts": {
         date: {"$toDate" : "2020-08-27T13:00:00Z"},
         iso8601: true
       }
    }
  }},
  {"$addFields": {
    "dateVarTrunc": { "$dateFromParts": {
      'isoWeekYear': "$dateVarFull.isoWeekYear",
      'isoWeek': "$dateVarFull.isoWeek",
      'isoDayOfWeek': 1
    }}
  }}
])

结果：

{
    "dateVarFull" : {
        "isoWeekYear" : NumberInt(2020), 
        "isoWeek" : NumberInt(35), 
        "isoDayOfWeek" : NumberInt(4), 
        "hour" : NumberInt(13), 
        "minute" : NumberInt(0), 
        "second" : NumberInt(0), 
        "millisecond" : NumberInt(0)
    }, 
    "dateVarTrunc" : ISODate("2020-08-24T00:00:00.000+0000")
}

可以通过对日期或时间戳字段进行算术运算来获得ISO周的开始，这里周的开始是Monday（1），周的结束是Sunday（7）

db.dd.aggregate(
    [
        {
            $addFields : { 
                startOfWeek : 1, // Monday
                currentDayOfWeek : {$dayOfWeek : "$date"}, 
                daysToMinus : { $subtract : [{$dayOfWeek : "$date"} , 1] },
                startOfThisWeek : { $subtract : [ "$date", {$multiply : [{ $subtract : [{$dayOfWeek : "$date"} , 1 ] }, 24, 60, 60, 1000 ]  } ] }
            }
        }
    ]
).pretty()

文件

> db.dd.find()
{ "_id" : ObjectId("5a62e2697702c6be61d672f4"), "date" : ISODate("2018-01-20T06:32:09.157Z") }

周开始

{
    "_id" : ObjectId("5a62e2697702c6be61d672f4"),
    "date" : ISODate("2018-01-20T06:32:09.157Z"),
    "startOfWeek" : 1,
    "currentDayOfWeek" : 7,
    "daysToMinus" : 6,
    "startOfThisWeek" : ISODate("2018-01-14T06:32:09.157Z")
}
>

可以使用$dateFromParts函数将日期截断为iso周：
举个例子

db.dd.aggregate(
  {
    $dateFromParts: {
      isoWeekYear: { $isoWeekYear: "$date" },
      isoWeek: { $isoWeek: "$date" }
    }
  }
)

对于Fri, 22 Jun 2018 20:46:50 UTC +00:00，它返回Fri, 18 Jun 2018 00:00:00 UTC +00:00。
要将日期截断为小时、日、月等，使用$dateFromString和$dateToString更容易。下面的示例将日期截断为小时：

db.dd.aggregate(
  {
    $dateFromString: {
      dateString: { 
        $dateToString: {
          format: '%Y-%m-%dT%H:00:00+00:00',
          date: '$date'
        }
      }
    }
  }
)

从Mongo 5开始，您的愿望已通过$dateTrunc运算符实现。
例如，将日期截断为年份：

// { date: ISODate("2021-12-05T13:20:56Z") }
// { date: ISODate("2019-04-27T05:00:32Z") }
db.collection.aggregate([
  { $project: { year: { $dateTrunc: { date: "$date", unit: "year" } } } }
])
// { year: ISODate("2021-01-01T00:00:00Z") }
// { year: ISODate("2019-01-01T00:00:00Z") }

您可以使用unit参数在不同级别的单位（年、月、日、小时...甚至季度）进行截断。对于给定的单位，可以使用binSize参数在不同的单位倍数（例如3年、6个月...）进行截断。
您还可以指定周的开始日期：

// { date: ISODate("2021-12-05T13:20:56Z") } <= Sunday
// { date: ISODate("2021-12-06T05:00:32Z") } <= Monday
db.collection.aggregate([
  { $project: {
    week: { $dateTrunc: { date: "$date", unit: "week", startOfWeek: "monday" } }
  }}
])
// { week: ISODate("2021-11-29T00:00:00Z") }
// { week: ISODate("2021-12-06T00:00:00Z") }