This term refers to a male bottom, particularly to the dirty state of his man pussy (hence the name 'shitty kitty'). His ass assumes this label upon discovery that his rectum was actually not completely empty, has been replenished by his sigmoid colon during the heat of passion and/or was never cleaned out to begin with. This is indicated by the presence of shit on the dick (or other object of insertion) of the unsuspecting top and/or the horrid stench of fresh shit.
This term may sometimes be heard during conversation between gay men regarding sexual encounters. "Obviously some guys aren't aware of the 'no shitty kitty' rule. Hello! No shitty kitties!"