Will Linux Mint Run Smoothly on My Old i7-6700k and GTX 1070 Setup?

I've been running Mint Cinnamon on some laptops with just 4 GB of RAM, and they work great! You shouldn't have any issues with your setup, it should handle Mint very smoothly.

Your computer is still solid! You don't even need to stick with Mint—there are plenty of distros with nice visuals that will run just fine. Performance drops you might have experienced on Windows are mostly due to software. If the hardware works, it’s nearly as good as new! Go for any desktop-oriented distro and you’ll be happy.

Definitely give it a shot! My experience might be different than yours, but I have a similar machine, and it runs just fine for me.

You'll likely be fine! Most of the Ubuntu-based distros will support your hardware. Your GTX 1070 will still get support from NVIDIA drivers for a bit longer. If you're not gaming on high-end titles, you'll be okay with Nouveau drivers as well. If you can, adding more RAM and tossing in an SSD will make a huge difference! I was doing 1080p video editing with similar specs up until recently, and it handled it well.

Hey, that's coincidentally my exact build! I switched to Pop!_OS and it's been fantastic. I bet Mint will work great for you too!