MIUI 7/8 has no way to disable the global Google Spell Check
Are you sure you enabled USB debugging on your phone? Is your phone listed when you enter "adb devices" in cmd? When you connect your phone to your PC, your phone should ask for a confirmation to start USB debugging.

The problem I had with these instructions was that my phone didn't actually connect to my PC, so ADB did not recognize the device.

After installing PDA-net on my PC, that issue was resolved. It installs the correct drivers.

Also make sure that in the USB debugging menu on your phone, you have enabled "USB debugging (security settings)" (you'll need a Mi account).

Then, enter adb shell, and settings put secure spell_checker_enabled 0. That should do it.

Complete instructions


Enable developer options on your phone (search for it in the settings app)
Enable USB debugging on your phone in the settings app
(This might not be required) Enable "USB debugging (security settings)" in the same menu.
Install ADB on your PC (use your favorite search engine to look up "ADB, Fastboot and Drivers - 15 seconds ADB Installer". I'm not allowed to post more than 3 URLs here)
Open a command prompt (cmd) and type cd [folder path where adb was installed].
Connect your phone through USB. Confirm USB debugging on your phone. If you don't get the confirmation window, download and install PDA-net on your PC.
Enter adb shell.
Enter settings put secure spell_checker_enabled 0. Done. Don't forget to disable USB debugging after you're done.