You want to sort rows in day-of-week order.

Use DAYOFWEEK() to convert a date column to its numeric day-of-week value.

Day-of-week sorting is similar to calendar-day sorting, except that you use different functions to get at the relevant ordering values.

You can get the day of the week using DAYNAME(), but that produces strings that sort lexically rather than in day-of-week order (Sunday, Monday, Tuesday, and so forth). Here the technique of displaying one value but sorting by another is useful (see Displaying One Set of Values While Sorting by Another). Display day names using DAYNAME(), but sort in day-of-week order using DAYOFWEEK(), which returns numeric values from 1 to 7 for Sunday through Saturday:

mysql>SELECT DAYNAME(date) AS day, date, description
    -> FROM event
    -> ORDER BY DAYOFWEEK(date);
+----------+------------+-------------------------------------+
| day      | date       | description                         |
+----------+------------+-------------------------------------+
| Sunday   | 1809-02-12 | Abraham Lincoln's birthday          |
| Sunday   | 1776-07-14 | Bastille Day                        |
| Monday   | 1215-06-15 | Signing of the Magna Carta          |
| Tuesday  | 1944-06-06 | D-Day at Normandy Beaches           |
| Thursday | 1989-11-09 | Opening of the Berlin Wall          |
| Friday   | 1732-02-22 | George Washington's birthday        |
| Friday   | 1958-01-31 | Explorer 1 launch date              |
| Friday   | 1957-10-04 | Sputnik launch date                 |
| Saturday | 1919-06-28 | Signing of the Treaty of Versailles |
| Saturday | 1789-07-04 | US Independence Day                 |
+----------+------------+-------------------------------------+

If you want to sort rows in day-of-week order but treat Monday as the first day of the week and Sunday as the last, you can use a the MOD() function to map Monday to 0, Tuesday to 1, ..., Sunday to 6:

mysql>SELECT DAYNAME(date), date, description
    -> FROM event
    -> ORDER BY MOD(DAYOFWEEK(date)+5, 7);
+---------------+------------+-------------------------------------+
| DAYNAME(date) | date       | description                         |
+---------------+------------+-------------------------------------+
| Monday        | 1215-06-15 | Signing of the Magna Carta          |
| Tuesday       | 1944-06-06 | D-Day at Normandy Beaches           |
| Thursday      | 1989-11-09 | Opening of the Berlin Wall          |
| Friday        | 1732-02-22 | George Washington's birthday        |
| Friday        | 1957-10-04 | Sputnik launch date                 |
| Friday        | 1958-01-31 | Explorer 1 launch date              |
| Saturday      | 1789-07-04 | US Independence Day                 |
| Saturday      | 1919-06-28 | Signing of the Treaty of Versailles |
| Sunday        | 1776-07-14 | Bastille Day                        |
| Sunday        | 1809-02-12 | Abraham Lincoln's birthday          |
+---------------+------------+-------------------------------------+

The following table shows the DAYOFWEEK() expressions to use for putting any day of the week first in the sort order:

Another function that you can use for day-of-week sorting is WEEKDAY(), although it returns a different set of values (0 for Monday through 6 for Sunday).