Hi Miro,
In short. There is a file in the SliTaz (like in any other Linux) that contains passwords. If you'll find a way to edit it, then you can reset passwords.
What the file? Actually there's two files: /etc/shadow and /etc/shadow-.
How to edit them? You can boot Live CD or Live USB on your machine. Or remove your hard disk and mount it to another machine with Linux installed. And you should be root super user.
If you copy shadow files from Live CD to your system, then you'll get default passwords (password root for root user, and empty password for tux user). Not bad if you copy current shadow files somewhere before you edit or substitute them.
You can edit files manually. Boot SliTaz Live CD, mount and open disk partition that contains your SliTaz installation using PCManFM. Click PCManFM's menu Tool -> Open Current Folder as Root, answer default root password. Go to your installed system folder (something like /media/your SliTaz/etc and edit shadow files by double click on them.
Each line begins with user name (login). Password contains between first and second colons (":" symbols) in the encoded form.
Note $1$EbR327ag$7NFmnOi7JQc5/lG0JLiU8/ means "root" password.
And empty password is nothing between :: in the "/etc/shadow" file and exclamation sign between :: (:!:) in the "/etc/shadow-" file.
Maybe I wrong, I just looked at files in my Live USB.
Good luck! And don't forget to change your passwords after successful boot onto your system!
PS. I'm reading this fine manual (RTFM) now:
http://linux.die.net/man/5/passwd
http://linux.die.net/man/5/shadow
Seems like "shadow-" is just a "previous" version of "shadow" file and you may not edit it.