I know that with at least the elementaryOS 5.0 "Juno" install media you are able to create custom partition tables.
Proceed through the installation wizard, and when you get to the "Installation Type" screen, select "Something else."
From here you can add/remove/change partitions.
If you're using a different version or are used to using other tools, you ...
Of course you can do it easily !
First of all, you need to create new partitions for eOS Distro (including his own swap if you have one for Mint (if both use the same swap, it's could have effect if you hibernate one and you boot the other one).
When you install eOS, or every linux distribution, by default an installation of grub is part of the linux distro ...
Can you please try hitting the 'e' key in the grub boot menu (text mode), and adding 'nomodeset=1' to the end of the line that starts with 'linux'. Then hit F10 to continue booting.
You should see something like:
(Googled image, not the exact line), Basically that's where I'm asking you to add the 'nomodeset=1' value at the end.