MySQL table partition truncation not to propagate on a slave
You do a TRUNCATE PARTITION on the Master daily, correct?  And you do not want that to be done on the Slave, correct?

If yes, then 

SET SQL_LOG_BIN = 0;
TRUNCATE ...;
SET SQL_LOG_BIN = 1;


https://dev.mysql.com/doc/refman/5.7/en/set-sql-log-bin.html

But, beware.  Once you have more than, say, 100 partitions, the table is likely to be slower and slower on the Slave.  And, at some point you will hit the maximum number of partitions.

I can't think of any thing that will "break" because of having more data (and more partitions) on the Slave than on the Master.  I assume you never otherwise modify the data in 'old' partitions.