This box will self destruct in x seconds.
Have a look at the UPS pico, if installed correctly you can use the automatic-power-down script (Automatic Files Safe Shutdown) that will shut the Pi down when the battery is low. You could mod the script to destroy data on the SD card before shutting down the PI.
You could then use the same "kill the SD card script" and add a small switch(button) to the inside of the box, connect it with the PI's GPIO pins and create a script that monitors the state of the switch. So if the box is opened while the Pi running, the switch is triggered and the card is destroyed.
UPS Pico ; https://pimodules.com/_pdf/13_0x40_W_UPS_PIco_HV3.0.pdf
PI GPIO ; http://raspberry.io/projects/view/reading-and-writing-from-gpio-ports-from-python/
The trouble would be that it will also destroy your card when the power goes down... You probably don't want that. And this setup just won't work when the PI's isn't even running....
I'd look into other options to keep data away from others, like encryption, this would solve the need for the Pi having to powered on and keep your data unreadable for people who have the SD card.
Encrypt ; https://github.com/NicoHood/NicoHood.github.io/wiki/Raspberry-Pi-Encrypt-Root-Partition-Tutorial
Or you could keep the data hidden in de cloud somewhere(like mega.nz/dropbox etc) and pull it when needed. If data isn't stored locally........
Encryption is proly the best way to go here, I'd say.