To remove Cortana, open Registry Editor and navigate to the following folder in the left-hand navigation pane: 
HKEY_LOCAL_MACHINE > Software > Policies > Microsoft > Windows > Windows Search.

	(If “Windows Search” does not exist, create a new key and name it "Windows Search".)

Inside the "Windows Search" key, create a new DWORD (32-bit) Value and name it “AllowCortana”.

Set “AllowCortana” to 0.

Close regedit and reboot.
 
(To enable Cortana again, reset "AllowCortana" to 1 and reboot.)