I fear you might be out of luck. Wayland is a display server which aims to become the replacement for X, so a pretty crucial bit of technology, and from what I can find, Mint 17 doesn't support it, despite being based on Ubuntu 14.04, which does. It looks like Mint purposefully prevents libwayland from being installed (that's just the support library for wayland, not wayland itself), and so when you manually choose to install it, that causes it to conflict with some crucial Mint packages which state that they're incompatible with wayland, causing a cascade of things being removed.
The two packages being upgraded,
libegl1-mesa and
libgbm1 both depend on wayland in their 14.04 incarnations. This suggest that Mint 17 manages to prevent wayland support by purposefully depending on earlier versions of those packages. It's a bit like a house of cards falling apart, here.
From what I can find, Mint 18 does support wayland, so upgrading (or moving to Ubuntu, which is doing a better job here with being consistent with package dependencies) might be an option? Otherwise there's ways to force installation of packages without adhering to their dependencies and conflicts, but that way lies madness.
It might be worth figuring out exactly where in the dependency tree the "conflicts" condition exists which causes all the uninstalls. Could be libwayland-egl1-mesa itself, but could also be one of the other packages to be installed. With that information, you might be able to limit the amount of madness caused by forcing an install of something.