I tried is as an exercise. Grabbed the netinst image of Debian Sid to ensure package compatibility with Mint's repositories. Installed the image and added the MATE environment + lightdm to login + xorg for basic graphical support. You may have an extra step for proprietary GPU drivers. At that point, you can switch all repos in sources.list from Debian to Mint, then update, upgrade, and reboot.
It still won't be clean, because the Mint devs provide a customized version of MATE that properly dresses up the desktop with a unified look and feel. It's difficult to approximate if you're gluing Debian and LMDE together. And you still need to install apps like a web browser, word processor, maybe a spreadsheet, GIMP, media player, email client, synaptic, etc.
This won't work with standard Debian images, because none of them come with MATE pre-installed. But if you don't care about MATE, then never mind.