MySQL 5.7

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CREATE TABLE table1 (
  `ID` VARCHAR(100),
  `Val` VARCHAR(100),
  `Val2` VARCHAR(100)
);
INSERT INTO table1
  (`ID`, `Val`, `Val2`)
VALUES
  ('606541','3175031503131004','3175032612900004'),
  ('606542','3175031503131004','3175032612900004'),
  ('677315','3175031503131004','3175032612980004'),
  ('222222','1111111111111111','8888888888888888'),
  ('231233','1111111111111111','3175032612900004'),
  ('111111','9999992222211111','1111111111111111'),
  ('57','3173012102121018','3173015101870020'),
  ('59','3173012102121018','3173021107460002'),
  ('2','900','7000'),
  ('4','900','7001');

Records: 10  Duplicates: 0  Warnings: 0


SELECT
	tb.* 
FROM
	table1 tb 
WHERE
	tb.Val2 IN (
	SELECT
		ta.Val2 
	FROM
		(
		SELECT
			t.* 
		FROM
			table1 t 
		WHERE
			t.Val IN ( 
			SELECT Val FROM table1 
			GROUP BY Val 
			HAVING count( Val ) > 1 ) 
		) ta 
	GROUP BY
		ta.Val2 
	HAVING
	count( ta.Val2 ) = 1 
	)


ID
Val
Val2


677315
3175031503131004
3175032612980004

222222
1111111111111111
8888888888888888

57
3173012102121018
3173015101870020

59
3173012102121018
3173021107460002

2
900
7000

4
900
7001


select t1.*from table1 t1 left join
      (select val from table1
       where val2 in (select val2 from table1 group by val2 having count(id) > 1)
        ) t2
 on t1.val = t2.val
 inner join
     (select val from table1 group by val having count(id) >1) t3
     on t1.val = t3.val
 where t2.val is null
        


ID
Val
Val2


57
3173012102121018
3173015101870020

59
3173012102121018
3173021107460002

2
900
7000

4
900
7001


select t1.*from table1 t1 inner join
       (select val from table1 group by val having count(id) = 1)
         t2
 on t1.val = t2.val
 inner join
     (select val2 from table1 group by val2 having count(id) >1) t3
     on t1.val2 = t3.val2


ID
Val
Val2

ID	Val	Val2
677315	3175031503131004	3175032612980004
222222	1111111111111111	8888888888888888
57	3173012102121018	3173015101870020
59	3173012102121018	3173021107460002
2	900	7000
4	900	7001