A bit later response but may help. In SQL 2016 MS introduced function DATEDIFF_BIG which will (according to type size) overflow in difference bigger than something like 290k years. But technet article have same time difference as basic DATEDIFF - https://msdn.microsoft.com/en-us/library/mt628058.aspx

See https://learn.microsoft.com/en-us/sql/t-sql/functions/datediff-transact-sql?view=sql-server-ver15#return-value
For millisecond, the maximum difference between startdate and enddate is 24 days, 20 hours, 31 minutes and 23.647 seconds.

If you need millisecond above that level, you'll need to write something custom.

In SQL Server 2016 there is a new function available: DATEDIFF_BIG

It solves exactly the overflow problem.

You don't need to refer to the miliseconds in your calculation.

This will do exactly the same as your script except the overflow:

SELECT CONVERT(varchar(12), 
        CAST('2014-11-04 08:21:17.723' as datetime) - 
        CAST('2014-08-04 10:37:28.713' as datetime)
       , 114)

For me there was a big interval between two dates so i have used below code
declare @timetagInMillsecond bigint=CAST(CAST( cast(@timetag as datetime) -'1970-01-01' AS decimal(38,10))2460601000+0.5 as bigint)

It works for me .

Use DATEDIFF_BIG to resolve the overflow issue

The datediff function resulted in an overflow. The number of dateparts separating two date/time instances is too large. Try to use datediff with a less precise datepart.

SELECT DATEDIFF_BIG( 
    millisecond, 
    SYSDATETIME(), 
    DATEADD(year, 1000, SYSDATETIME()) ) AS 'Milliseconds in 1000 years';

For SQL Server 2014, the following works around the 'int' limitation to obtain a "JavaScript Time Epoch". This assumes the start epoch is itself a date, which fits the local use-case leading to finding this question. The query requires adaptation to the specific question use-case which does not have this property.

declare @x as datetime = getdate()

-- epoch_delta_s_to_date * 1000 + day_delta_ms
select
cast(datediff(second, '1970-01-01', cast(@x as date)) as bigint) * 1000
  + cast(datediff(millisecond, cast(@x as date), @x) as bigint)

For the case of obtaining a "JavaScript Time Epoch" this is still subject to the Y2038 limitation of datediff(second, '1970-01-01', ..) .

I have to use DATEDIFF_BIG in SQL versions before SQL2016 and have written my own function:

Declare @datestart datetime = '1953-01-01 23:18:09.284'
Declare @dateend datetime = '9999-12-31 23:54:03.844'

select 
/*DATEDIFF_BIG(millisecond, @datestart, @dateend) AS [ForTestComparion], */
(cast(DATEDIFF(DAY, @datestart, @dateend) as bigint) * 24 * 60 * 60 * 1000 )
+ 
    DATEDIFF(millisecond, 
    DATETIMEFROMPARTS(2000, 1, 1,DATEPART(HOUR, @datestart), DATEPART(MINUTE, @datestart), DATEPART(SECOND, @datestart), DATEPART(MILLISECOND, @datestart)),
    DATETIMEFROMPARTS(2000, 1, 1,DATEPART(HOUR, @dateend), DATEPART(MINUTE, @dateend), DATEPART(SECOND, @dateend), DATEPART(MILLISECOND, @dateend)))

2000, 1, 1 can be any date just need to be same day to compare only hours,minute,second,milisecond