1, see the slow log status;
mysql> show variables like '%slow%';
+---------------------+------------------------------------------+
| Variable_name | Value |
+---------------------+------------------------------------------+
| log_slow_queries | ON |
| slow_launch_time | 2 |
| slow_query_log | ON |
| slow_query_log_file | /mysqllog/slow_log/slow_queries_3306.log |
+---------------------+------------------------------------------+
4 rows in set (0.00 sec)

2, stop the slow log server.
mysql> set global slow_query_log=0;
Query OK, 0 rows affected (0.27 sec)

mysql> show variables like '%slow%';
+---------------------+------------------------------------------+
| Variable_name | Value |
+---------------------+------------------------------------------+
| log_slow_queries | OFF |
| slow_launch_time | 2 |
| slow_query_log | OFF |
| slow_query_log_file | /mysqllog/slow_log/slow_queries_3306.log |
+---------------------+------------------------------------------+
4 rows in set (0.00 sec)

mysql>
mysql> show variables like '%slow%'; -- check slow log status
+---------------------+------------------------------------------+
| Variable_name | Value |
+---------------------+------------------------------------------+
| log_slow_queries | OFF |
| slow_launch_time | 2 |
| slow_query_log | OFF |
| slow_query_log_file | /mysqllog/slow_log/slow_queries_3306.log |
+---------------------+------------------------------------------+
4 rows in set (0.00 sec)

3, reset the new path of slow log
mysql> set global slow_query_log_file='/mysqllog/slow_log/slow_queries_3306_new.log';
Query OK, 0 rows affected (0.03 sec)

4, start the slow log server
mysql>
mysql>
mysql> set global slow_query_log=1;
Query OK, 0 rows affected (0.01 sec)

mysql> show variables like '%slow%';
+---------------------+----------------------------------------------+
| Variable_name | Value |
+---------------------+----------------------------------------------+
| log_slow_queries | ON |
| slow_launch_time | 2 |
| slow_query_log | ON |
| slow_query_log_file | /mysqllog/slow_log/slow_queries_3306_new.log |
+---------------------+----------------------------------------------+
4 rows in set (0.00 sec)

5, check the slow sql in the new slow log file.
mysql> select sleep(10) as a, 1 as b;
+---+---+
| a | b |
+---+---+
| 0 | 1 |
+---+---+
1 row in set (10.00 sec)

mysql>
[mysql@xxx-xxx ~]$ more /mysqllog/slow_log/slow_queries_3306_new.log
......
Time Id Command Argument
# Time: 140213 6:44:24
# User@Host: root[root] @ localhost []
# Query_time: 10.000365 Lock_time: 0.000000 Rows_sent: 1 Rows_examined: 0
SET timestamp=1392273864;
select sleep(10) as a, 1 as b;

6, backup the old big slow log file to other directory.
mv /mysqllog/slow_log/slow_queries_3306.log /mysqlbackup/slow_log/slow_queries_3306.log.bak.20140213