Look: I'm not really happy running Windows Server to begin with [HN crowd: a decision that was not mine, by the way], so why do you have to have this stupid thing downloading and running all kinds of random executables that I have no idea what they do in my bloody server farm? And yup, I have logs off all those things, and pager traffic as a witness.
Yes, you can turn Cortana off. No, you shouldn't have to. This decision beggars the imagination.
(I like to think that the PM behind Cortana-makes-sense-in-a-server was the same nimrod who also shipped the touchscreen support in Server 2012R2 and the all-caps menu nonsense that plagued Visual Studio and Office for a few years, until Microsoft got a clue and realized they were honestly, really and truly pissing off customers. Someone needs to take that person out back of Building 9 and show them the instruments).