The suite of Office apps, including Word, Excel, PowerPoint, and the others, also have an independent spell checker, which you can easily disable. However, OneNote doesn't even have options to control spelling. OneNote also doesn't respond to the Windows 10 Spelling feature. For example, if you want to disable spell checking on the new Windows 10 Mail app, you'll need to open Mail, click on New Mail, navigate to Options, and change the Spelling options. It's worth pointing out that surprisingly, even though the spell checker is a global feature, many apps work independently. You can always enable the settings back by coming back to the Typing Settings section. That's all you have to do to disable the spell checker in Windows 10.
Quick Note: If you're disabling the spelling options while the apps are still running, you'll need to restart the app you want to use without the autocorrect in order the changes to take effect.