SET @date = '2000-01-01';
WHILE @date < 'требуемая дата'
DELETE FROM table WHERE `date` = @date;
SET @date = @date + INTERVAL 1 DAY;
END WHILE;

mysql> CREATE TABLE `table` (`date` DATETIME);
Query OK, 0 rows affected (0.45 sec)

mysql> INSERT INTO `table`
    -> SELECT '2015-01-01' UNION ALL
    -> SELECT '2015-01-10' UNION ALL
    -> SELECT '2015-01-20' UNION ALL
    -> SELECT '2015-01-30' UNION ALL
    -> SELECT '2015-02-01' UNION ALL
    -> SELECT '2015-02-02' ;
Query OK, 6 rows affected (0.09 sec)
Records: 6  Duplicates: 0  Warnings: 0

mysql> DELIMITER $$
mysql> CREATE PROCEDURE MyDelete()
    -> BEGIN
    -> SET @date = '2015-01-10';
    -> WHILE @date < '2015-02-01' DO
    -> DELETE FROM `table` WHERE `date` = @date;
    -> SET @date = @date + INTERVAL 1 DAY;
    -> END WHILE;
    -> END;
    -> $$
Query OK, 0 rows affected (0.10 sec)

mysql> DELIMITER ;
mysql> SELECT * FROM `table`;
+---------------------+
| date                |
+---------------------+
| 2015-01-01 00:00:00 |
| 2015-01-10 00:00:00 |
| 2015-01-20 00:00:00 |
| 2015-01-30 00:00:00 |
| 2015-02-01 00:00:00 |
| 2015-02-02 00:00:00 |
+---------------------+
6 rows in set (0.02 sec)

mysql> CALL MyDelete;
Query OK, 0 rows affected (0.15 sec)

mysql> SELECT * FROM `table`;
+---------------------+
| date                |
+---------------------+
| 2015-01-01 00:00:00 |
| 2015-02-01 00:00:00 |
| 2015-02-02 00:00:00 |
+---------------------+
3 rows in set (0.00 sec)