Mirror the device? No, not possible. But you could use an HDMI splitter and send the Roku output to both TVs. Of course, the distance needs to be reasonable, and obviously you need to run a cable between them. That said, there are ways to send HDMI wirelessly between two points. It sounds like both TVs are in the same room, so distance shouldn't be an issue. But if it's not really possible to run an HDMI cable between the two, it might be an option.
Here's an interesting option. Not only does it stream the HDMI wirelessly to the receiving unit, it appears the transmitting unit also has an HDMI out to feed the first TV. So an HDMI splitter isn't necessary.
Just note that these devices are all likely going to be 1080p max. No 4K without paying a lot more money, assuming there even are any.
Dan Roku Stick (3600), Ultra (4640), Ultra (4670), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.