This was the first Rugrats episode to depict blood on screen. It certainly was not the first Nicktoon to depict blood; Ren & Stimpy, Doug and Rocko's Modern Life have all depicted blood but in a non-violent manner.
Goof: Throughout the entire episode "The First Cut" Tommy's band aid keeps disappearing and then reappearing.
Tommy: Was there... lots of blood?
Angelica: Oh, it got all over Mommy's dress I was accidentally wearing.
Angelica: Can we get a sewing machine out here?