In order to keep the disk usage of the binlogs down while having replication, it is necessary to periodically perform a PURGE BINARY LOGS command.

Please keep in mind that it is important to ensure that you don’t remove any binlogs that are still needed by the replicas.

For example:
PURGE BINARY LOGS BEFORE '2008-04-02 22:46:26';

You can read more about this command here: