even if I cut down the data up to maximum permissible length (using LEFT function, or SUBSTRING , or whatever), the insert fails for some data

With LEFT or SUBSTRING you are cutting it down to the specified number of characters, whereas the 10 in varchar(10) specifies the number of bytes, so after your truncation with LEFT or SUBSTRING you are left with a string that may still have more bytes than 10 - which is the same, for the purpose of insertion, as if you never truncated it in the first place.

A simple way to truncate the string to a number of characters rather than bytes is to use CAST or CONVERT , because they cut the string before the surrogate pair that doesn't fit and keep the original collation:

INSERT INTO [#tmpdl] ([Txt]) VALUES (cast(N'123456789ábcd' COLLATE Czech_100_CI_AS_SC_UTF8 as varchar(10)));
INSERT INTO [#tmpdl] ([Txt]) VALUES (cast(N'一二三四' COLLATE Czech_100_CI_AS_SC_UTF8 as varchar(10)));

Do note that this requires SQL Server 2012 or later.

The 10 for a UTF8 value denotes the bytes that can be stored in the data type, not the number of characters. For the value '123456789abcd' these are all ANSI characters and 1 bytes in size. For '123456789ábcd' , however, the character á is 2 bytes in size; this makes the datalength of the string you try to INSERT 11 bytes, not 10. It's a similar story for your last string, '一二三四' :

SELECT V.YourString,
       DATALENGTH(V.YourString),
       DATALENGTH(LEFT(V.YourString,10))
FROM (VALUES('123456789abcd' COLLATE Czech_100_CI_AS_SC_UTF8),
            (CONVERT(varchar(20),N'123456789ábcd' COLLATE Czech_100_CI_AS_SC_UTF8)),
            (CONVERT(varchar(20),N'一二三四' COLLATE Czech_100_CI_AS_SC_UTF8)))V(YourString);

You need to ensure that the length of the column you define has enough space for all the bytes, not the number of characters:

DROP TABLE IF EXISTS #tmpdl
GO
CREATE TABLE [#tmpdl] ([Txt] VARCHAR(12) COLLATE Czech_100_CI_AS_SC_UTF8 NULL)
GO
INSERT INTO [#tmpdl] ([Txt]) VALUES (LEFT('123456789abcd', 10)) --this works
GO
INSERT INTO [#tmpdl] ([Txt]) VALUES (LEFT('123456789ábcd', 10)) --this fails
GO
INSERT INTO [#tmpdl] ([Txt]) VALUES (LEFT(N'一二三四', 10)) --this also fails
GO
SELECT *
FROM  #tmpdl;
GO
DROP TABLE #tmpdl