You'll need to go to the command line, go into the Armory directory, and manually start Armory. Here's an example. It assumes Armory is in /Applications, and that
/Applications/Armory.app/Contents/MacOS is your terminal's working directory.
./Armory --datadir=/Volumes/ExtDriveName/ArmoryDataLocation --satoshi-datadir=/Volumes/ExtDriveName/BitcoinCoreDataLocation
There are ways to automate this but focus on getting this to run manually for now.
ExtDriveName is actually whatever your drive is called, and
ArmoryDataLocation and
BitcoinCoreDataLocation are the directories where the respective data resides.