Just download the app as a .tar.gz. It's that easy.
I don't have a Mac, but it appears that you just have to extract the DMG
First, run the regular discord installer.
Then go to %LOCALAPPDATA\Discord and copy the folder to wherever you want. Rename it if you want to.
Now go to Control Panel > Programs and Features and uninstall Discord. Now go to [the discord folder]\app-[version] (where [the discord folder] is where you copied the Discord folder and [version] is the app version,, there should be only one directory in that format anyways, correct me if I'm wrong though)and click on Discord.exe. Discord should start if you did this correctly.
I'm not sure how portable this is as I haven't tested this on computers that haven't gone through the install process yet, but it should work on your current computer.