I once downgraded from Windows 8 Pro with Media center to Windows 8 Pro without media center. I did this by changing a registry value that holds the operating system details. This may/may not work to downgrade from Windows 10 to Windows 8.1, but try this (at your own risk):
1. Do Windows Key + R (will open run dialog)
2. Type regedit and then enter
3. In the reg editor, navigate to this key on the left side: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion
4. On the right side you should see to values EditionID And ProductName. Note down their values because these are the ones you have to change. If this fails then you will have to revert these strings to their original values.
5. Change these values to: EditionID = "Core", ProductName= "Windows 8" (Without the quotes)
6. Now insert your Windows 8.1 Installation DVD. (if you don't have one then you can download the iso file from some website. This is legal if you own Windows 8.1. Then you can burn it to a dvd or create a bootable usb flash drive out of it.)
7. Follow the instructions, then enter your product key, then check keep all my windows settings files and apps (the first option)
8. The installation will proceed (maybe) and then you may get windows 8.1 back. Your windows 10 installation will be moved to Windows.old and you can delete it to free some hard drive space.