Completely removing Wine can be harder than just removing it from the Synaptic package manager. You can even delete the hidden .wine folder in your home directory and still have Wine configuration files left behind. So in case you want to completely remove Wine, simply copy and paste the following in the terminal. It will uninstall Wine and remove it from the menu as well.
sudo apt-get remove wine
rm -rf $HOME/.wine
rm -f $HOME/.config/menus/applications-merged/wine*
rm -rf $HOME/.local/share/applications/wine
rm -f $HOME/.local/share/desktop-directories/wine*
rm -f $HOME/.local/share/icons/????_*.xpm
Then you can reinstall it if you so desire.