I think I will find a solution by playing a little.
It seems that the Valet uninstall does not work as expected. To remove it, first run the composer command to remove the php dependencies:
$ composer global remove laravel/valet
then to remove the dependencies installed with Homebrew, first run
$ brew list
so that you know that we are on the same page, then if you see dnsmasq and php70 in case you do not want them, or you have php7 installed in a different approach (for example, me):
$ brew uninstall dnsmasq
and
$ brew uninstall php70
Then go to your user directory and delete the hidden .valet directory or run the terminal command as follows:
$ sudo rm -r ~/.valet
source share