MySQL 8.0

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create table test (t1 datetime, t2 datetime default '2020-06-27 00:00:00')
insert into test (t1) values
('2020-06-27 00:01:39'), 
('2020-06-27 04:01:39'), 
('2020-06-27 00:21:39'), 
('2020-06-27 00:00:09'), 
('2020-06-28 00:00:00'), 
('2020-06-28 04:03:02'), 
('2020-06-27 00:00:00')
SELECT TIMEDIFF(t1, t2),
       TRIM(LEADING '0' FROM TRIM(LEADING '00:' FROM TIMEDIFF(t1, t2))) AS trimmed,
       REGEXP_REPLACE(TIMEDIFF(t1, t2), '^[0:]+(\\d)', '$1') AS regexed,
       IF(TIMEDIFF(t1, t2) = '00:00:00', 0, TRIM(LEADING '0' FROM TRIM(LEADING '00:' FROM TIMEDIFF(t1, t2)))) AS ctrim
FROM test


TIMEDIFF(t1, t2)
trimmed
regexed
ctrim


00:01:39
1:39
1:39
1:39

04:01:39
4:01:39
4:01:39
4:01:39

00:21:39
21:39
21:39
21:39

00:00:09
9
9
9

24:00:00
24:00:00
24:00:00
24:00:00

28:03:02
28:03:02
28:03:02
28:03:02

00:00:00

0
0

TIMEDIFF(t1, t2)	trimmed	regexed	ctrim
00:01:39	1:39	1:39	1:39
04:01:39	4:01:39	4:01:39	4:01:39
00:21:39	21:39	21:39	21:39
00:00:09	9	9	9
24:00:00	24:00:00	24:00:00	24:00:00
28:03:02	28:03:02	28:03:02	28:03:02
00:00:00		0	0