demo, MySQL - rextester

Language: Layout:

#MySQL 5.7.12
#please drop objects you've created at the end of the script 
#or check for their existance before creating
#'\\' is a delimiter

DROP TABLE IF EXISTS contacts;
CREATE TABLE contacts (Date varchar(55));
INSERT INTO contacts (Date)
VALUES
    ('2017/9/2'),
    ('2017/9/11'),
    ('2017/8/7'),
    ('2017/8/12'),
    ('2017/8/11'),
    ('2017/8/10'),
    ('2017/7/21'),
    ('2017/6/27'),
    ('2017/6/26'),
    ('2017/6/24'),
    ('2017/6/23'),
    ('2017/6/22');

SELECT *
FROM contacts
ORDER BY Date DESC;

SELECT
    Date,
    SUBSTR(Date, 1, 4) AS year,
    CASE WHEN INSTR(SUBSTR(Date, 6), '/') = 2
         THEN CONCAT('0', SUBSTR(Date, 6, 1))
         ELSE SUBSTR(Date, 6, 2) END AS month,
    CASE WHEN LENGTH(SUBSTR(SUBSTR(Date, 6), INSTR(SUBSTR(Date, 6), '/') + 1)) = 1
         THEN CONCAT('0',SUBSTR(SUBSTR(Date, 6), INSTR(SUBSTR(Date, 6), '/') + 1))
         ELSE SUBSTR(SUBSTR(Date, 6), INSTR(SUBSTR(Date, 6), '/') + 1) END AS day
FROM contacts
ORDER BY
    SUBSTR(Date, 1, 4) DESC,
    CASE WHEN INSTR(SUBSTR(Date, 6), '/') = 2
         THEN CONCAT('0', SUBSTR(Date, 6, 1))
         ELSE SUBSTR(Date, 6, 2) END DESC,
    CASE WHEN LENGTH(SUBSTR(SUBSTR(Date, 6), INSTR(SUBSTR(Date, 6), '/') + 1)) = 1
         THEN CONCAT('0', SUBSTR(SUBSTR(Date, 6), INSTR(SUBSTR(Date, 6), '/') + 1))
         ELSE SUBSTR(SUBSTR(Date, 6), INSTR(SUBSTR(Date, 6), '/') + 1) END DESC;


absolute service time: 0,33 sec