LTC2400 ADC apply on Arduino Due

But I was trying to set both low for the most of time. SD is low all the time, ADC is low when it's doing work.
I will need them both low to work at the same time. Is that possible?

A chip select signal is LOW active which means that the chip is activated on LOW and deactivated on HIGH. So you have to try to let the chip select lines be HIGH as often as possible.
Only one of them must be low at any given time because else you're sending commands to multiple devices which may even result in short circuits on the MISO line.