When you installed Linux Mint Debian Edition (LMDE), you may have noticed that there is no "Additional Drivers" program. But don't worry, you can install the driver and the Catalyst Control Center. Just follow these steps:
Open the Terminal and type these commands:
sudo apt-get remove --purge fglrx*
sudo apt-get update && sudo apt-get install fglrx-driver fglrx-control
sudo /usr/bin/aticonfig --initial
And then reboot your system. You're good to go!