The term "Sukkana sukkana!" is closely related to this, being again type of finnish drunken engouragement, usually to get individual drink whole open container of alcoholic beverage (usually beer) with one big gulp. Not be taken usually as offensive as "Ässysy".
Person1: "Soo lets get totally shitfaced tonight!!"
Person2: "Well, I think I gotta get home early, and I dont really wanna be again, you know, like vomiting all over myself"
Person1: "What!!? Are you some kind of pussy?? Lets get this thing going! Now grab your drink! Down the hatch!! Ässysy äsysy äsysy!!"