The new FireTV sticks don't have the option for Mirroring at all.
But there's nothing to worry about and there seems to be a workaround for that.
Firstly, you'll need the CastApp to be installed on your FireTV Stick.
You can download the CastApp from this direct download link.
If the link does not work you can get it from the XDA forum thread here. Or https://forum.xda-developers.com/fire-tv/general/chrome-cast-receiver-fire-tv-t3708913
Once downloaded you need to install it in your FireTV stick. To do that either install adblink from this tutorial or transfer it to FireTV stick using ES File Explorer like most of the people do.
Once installed open the application and check Google Cast.
Now open Google Chrome web browser.
Click on the menu button on the top right and click on Cast...
After that click on down arrow Cast to.
And select Cast desktop
And then select your FireTV Stick
Sometimes you might note that it won't find your FireTV Stick in the list. To fix that just untick Google Cast in CastApp Settings and check it back.
This application not only works for desktop but your mobile phone as well.