What caused the huge drop of the mempool from 60 MB to Less then 1 MB?
These transaction didn't get processed there was no 60 MB block mined at the time.
This occurred at 10:38 pm 29th August 2017 NZ time
It didn't goto zero. You can look at alternate sources https://core.jochen-hoenicke.de/queue/#2d . What happened most probably is that blockchain.info's node went down/rebooted momentarily.
It looks like the node whose mempool size is used to generate this chart was rebooted. Also, this node appears to be running an old version of Core or another node software, because recent versions of Core persist the mempool across restarts.
65000 transactions is subtracted. They are still there (55441+14199) as long they are not canceled. The reason of subtraction seems to be too low fees, lesser than 30 satoshi. Maybe blockchain.info do not want to count "spam and attacks" in the statistics? It happened around 12:00 here in sweden. And a break out +$200 in Bitcoin price followed around 15:30.
The pools are only in the nodes. What they do when it gets full is up to them.