Is there a way to turn auto-downloading off on my Mac?

Apple does not initiate macOS updates if there is low space but the case is different when enough space is there. It is problematic sometimes. Your question is very simple. You are looking forward to turning off this auto-downloading feature. For your benefit, we have come with a reliable solution. So, an open invitation to learn the procedure is shared with you, throughout this page.  

1. Open your Mac
2. Go to System Preferences
3. Select App Store
4. Find [Download newly available updates in the background]
5. Deselect it
6. Mac will now notify you when macOS software updates

It will also update to your installed apps (that are available) but won’t download them automatically in the background unless you tell it to. Obviously, you will receive notification if an update is available. Even if you have disabled this feature you can easily check for updates manually. The [Updatestab] is likely to make your job easier in this regard. How to manage other auto updates is obviously the next question you are going to ask. Select [Install macOS updates] if you want downloaded macOS updates to install automatically. However, you can select [Install app updates] for allowing the computer to install any app updates from the Mac App Store automatically. The [Install system data files and security updates] option can be activated for the enhancement of security.