我不明白你到底在找什么，所以这里有一个不完整的解决方案。。。

DROP TABLE employee_assignments;

CREATE TABLE employee_assignments
(day CHAR(3) NOT NULL PRIMARY KEY
,total_working_hours INT NOT NULL DEFAULT 0
);

INSERT INTO employee_assignments VALUES
('mon',10),
('tue',10),
('wed',10),
('thu',10),
('fri',10),
('sat',0),
('sun',0);

DROP TABLE timesheet;

CREATE TABLE timesheet
(start DATETIME NOT NULL PRIMARY KEY
,end  DATETIME NOT NULL 
);

INSERT INTO timesheet VALUES
('2018-07-02 00:28:29','2018-07-02 04:12:17'),
('2018-07-05 00:26:20','2018-07-05 05:03:23'),
('2018-07-12 00:27:35','2018-07-12 10:21:08');

SELECT t.*
     , (TIME_TO_SEC(t.end)-TIME_TO_SEC(t.start))/3600 n 
     , a.*
  FROM timesheet t
  JOIN employee_assignments a
    ON a.day = DATE_FORMAT(t.start,'%a');

+---------------------+---------------------+--------+-----+---------------------+
| start               | end                 | n      | day | total_working_hours |
+---------------------+---------------------+--------+-----+---------------------+
| 2018-07-02 00:28:29 | 2018-07-02 04:12:17 | 3.7300 | mon |                  10 |
| 2018-07-05 00:26:20 | 2018-07-05 05:03:23 | 4.6175 | thu |                  10 |
| 2018-07-12 00:27:35 | 2018-07-12 10:21:08 | 9.8925 | thu |                  10 |
+---------------------+---------------------+--------+-----+---------------------+

我参考手册找到了一个办法。但看起来很乱。

SELECT
    start,
    end,
    total_hours_worked
FROM mytable
GROUP BY DATE(start), DATE(end)
having CASE 
    WHEN DAYOFWEEK(MIN(start))=1 and total_hours_worked < 0   THEN 1 
    WHEN DAYOFWEEK(MIN(start))=2 and total_hours_worked < 10  THEN 1 
    WHEN DAYOFWEEK(MIN(start))=3 and total_hours_worked < 10  THEN 1 
    WHEN DAYOFWEEK(MIN(start))=4 and total_hours_worked < 10  THEN 1 
    WHEN DAYOFWEEK(MIN(start))=5 and total_hours_worked < 10  THEN 1 
    WHEN DAYOFWEEK(MIN(start))=6 and total_hours_worked < 10  THEN 1 
    WHEN DAYOFWEEK(MIN(start))=7 and total_hours_worked < 0   THEN 1 
    ELSE 0 
END;