'stugatz' should really be written 'stu cazz' (like the lawyer Stewart Katz)
It would be considered a short form and dialect for 'questo cazzo'. It literally means 'this cock/dick/penis'. As you say it, you also point to your own cock with either one or two open hands. It is as if you are saying to the person or persons in front of you to "Suck my dick!" Hope this helps...