MySQL Purge binlog Safely

First of all, please check slave server status with the SQL query below:

show slave status;

look for the "Relay_Master_Log_File" column, and see which master binlog the slave had replicated up to.

example data: mysql-bin.000096

At your master 

mysql> PURGE BINARY LOGS TO 'mysql-bin.000096';

Master will clean up the mysql binlog up to mysql-bin.000096 ( the file with this name will still remain there)