I don't know anything about the Homebrew installer of Hammerspoon, so I don't know where it actually stores the application itself, but your Hammerspoon configuration files should be in `~/.hammerspoon`. The easiest way to completely remove them is to open a window in the `Terminal` application and type `rm -r ~/.hammerspoon` (note that this deletes them completely... if you'd rather move them out of the way in case you want to try again later, you can do something like `mv ~/.hammerspoon ~/Desktop/hammerspoon_config` to put them into a folder on your desktop that you can then store or delete later as you wish.)
You can also stop Hammerspoon from auto-starting by opening up System Preferences, select "Users & Groups", then click on the "Login Items" tab. From the list that comes up, select Hammerspoon and then click on the minus sign at the bottom of the list to remove it.
Of course, if Hammerspoon is still showing up in that list, Homebrew hasn't fully removed it, so you've still got that issue to figure out.
Hope this helps at least some!