Van Dennis' GPEdit instructions are correct, but the reboot isn't necessary.
- Open Command Prompt as an Administrator, then type "gpedit" (you'll want to open it like that if you're not working from an Admin account. If you are on an Admin account, typing "gpedit" in the search bar on the taskbar opens it)
- In the bar on the left, expand the trees for Computer Configuration --> Administrative Templates --> Windows Components --> News and Interests
- "Enable news and interests on the taskbar" should be listed on the body of the window.
- Double Click "Enable news and interests on the taskbar", then click "Disabled"
To put this into effect you can restart your computer if you'd like. If you don't want to reboot and/or can't at the moment:
- In Command Prompt as an Admin, type "gpupdate /force"
- Once that completes, restart Explorer.exe. "Windows Explorer" in the Task Manager should have a restart button on the bottom right of the manager, otherwise you can taskkill /f /im explorer.exe in Command Prompt to kill it then just "explorer" (without the .exe) to start it in Command Prompt).
It should be noted, though, that this only hides the service from the taskbar. It does not actually remove the service. Because it's probably more bloat built into Cortana, I'm not sure if there's a good way to remove the service without bricking you toolbar and search capabilities.