The eximstats database might tend to grow in size if there is high amount of mailing from your server.

Check if the following value from WHM is set to a higher interval :

Home »Server Configuration »Tweak Settings

>> “The interval, in days, to retain Exim stats in the database”

You might need to reduce the time interval to retain the eximstats.

Under usual situation, eximstats will grow huge in size when there is spamming carried out from your server. First check if your server is involved in spamming and if so, find the source of spamming and eradicate it.

You can remove the eximstats mysql db as follows :

# mysql -u root -p
# use eximstats
# delete from sends;
# delete from smtp;
# delete from failures;
# delete from defers;

If the above tends to consume lots of time, you can use the below commands to clear eximstats :

# mysqladmin drop eximstats

# mysqladmin create eximstats

# mysql eximstats < /usr/local/cpanel/etc/eximstats_db.sql