How to remove snap store from Ubuntu?

The package is not called snap, but instead is snapd.

You will want to do

sudo apt autoremove --purge snapd

TL;DR:

sudo rm -rf /var/cache/snapd/

sudo apt autoremove --purge snapd gnome-software-plugin-snap

rm -fr ~/snap

This will completely remove snap, snapd, all installed snap packages and their data, and never again suggest snap packages in the software store.

Your output of mount, df and cat /proc/partitions will thank you ;)

I'm not sure if you asked espacially for this, but if you just want to remove showing snap packages in Software (gnome-software; as I wanted to), you can just uninstall snap plugin with command sudo apt-get remove --purge gnome-software-plugin-snap.
I don't know if --purge is necessary, but it works fine - Software doesn't show now packages from Snap Store, but I can still install them by commandline with snap install [something]