Microsoft has made it difficult to disable Cortana, although it was a toggle to turn Cortana off in Windows 10 this is removed in the Anniversary Update.
You will need to jump into the registry;
(If “Windows Search” key doesn’t exist create it)
Add a new REG_DWORD (32-bit Value) “AllowCortana” value is “0” in Windows Search
You’ll have to sign out and sign back in, or restart, for the change to take place.
Cortana will (may?) still be running but seems to be limited to the Windows 10 search functionality.
* There is a Group Policy available for Enterprise users
Computer Configuration > Administrative Templates > Windows Components > Search
Set ‘Allow Cortana’ to “Disabled”