First disable it, then uninstall the Cortana app.
Disable it in the search settings:
1> Click the search icon/box in the bottom left
2> click the gear on the left bar
3> Click off next to Cortana/Web Searches

Then uninstall it, as listed here:
In elevated powershell:
Get-AppxPackage | Select Name, PackageFullName
Remove-AppxPackage Microsoft.Windows.Cortana_1.4.8.176_neutral_neutral_cw5n1h2txyewy
This is similar to MC10's answer, except that I'm sure the OS will be more accepting of uninstalling it via the "proper channels" (powershell) instead of renaming the folder.
Windows has fixed it so now you cannot remove "...Cortana_1.6.1.52_ ...". When this is attempted it states this is part of Windows now and cannot be removed. I guess I will go back to renaming the folder.
I'm using the same uninstall to remove other "features" like BingNews, BingSports, Etc
Edit: Likewise, you can remove the "Provisioned" applications (aka: crap that gets installed per user) via this method
Get-AppxProvisionedPackage -Online | Select DisplayName, PackageName
Remove-AppxProvisionedPackage Microsoft.ZuneMusic_2019.6.11821.0_neutral_~_8wekyb3d8bbwe
Or... to remove ALL Apps that you can, app or provisionedapp, you can do this:
Just a warning: This will uninstall the Windows Store. That's not an issue for me, but uninstalling everything isn't for the faint of heart.
Get-AppxPackage | Remove-AppxPackage
Get-AppxProvisionedPackage -Online | Remove-AppxProvisionedPackage -online
As mentioned in comments, it's probably wise not to completely remove the windows store. I haven't tried this yet, but this (in the comments) looks to be ballpark of what I'd use:
Get-AppxPackage -AllUsers | where-object {$_.name –notlike "*store*"} | Remove-AppxPackage
Get-appxprovisionedpackage –online | where-object {$_.packagename –notlike "*store*"} | Remove-AppxProvisionedPackage -online
Further resource: Delete Windows 10 Apps and Restore Default Windows 10 Apps
WinKey+start typing to find appquite often I needed do re-enable Cortana. Thanks M$... seems you haven't learned from IE lawsuit in 90s. – kape123 Mar 15 at 8:11