mysqldump with --where clause is not working

You may need to use quotes:

mysqldump -t -u root -p  mytestdb mytable --where="datetime LIKE '2014-09%'"

Selecting dates using LIKE is not a good idea. I saw this method in one project. This causes huge DBMS load and slow system operation as no index by this table column used.

If you need to select date range use between:

where datetime between '2014-09-01' and '2014-09-30 23:59:59'