I configured my previous PC that way. I set it up that way during installation. I put /home on the HDD, and everything else on the SSD. This meant that files just go to the right drive by default.
I did have to create a folder on the SSD and change the permissions so steam could put games there. Steam does not have root admin access.
This is an advanced configuration, but you can manage it. Since its during installation, you're wiping the disks so there's little risk in trying it again if you don't get it right on the first try. Linux Mint's installer has the tools and instructions on how to do this.
The directory structure on Linux works very differently from windows. Things can be linked and everything is a file, and the location of something in the directory structure doesn't match the hardware its on.
/ is the root directory of the system. /home is where all your files are stored. Select "something else" during the Mint installation and manually set up partitions, to put / on the SSD, and /home on the HDD and it should just work.