Is this the scene with the mobster when he pretended to be dead?
"Wanna know how I got these scars? My father was... a drinker. And a fiend. And one night he goes off crazier than usual. Mommy gets the kitchen knife to defend herself. He doesn't like that. Not-one-bit. So - me watching - he takes the knife to her, laughing while he does it! Turns to me, and he says, "why so serious, son?" Comes at me with the knife... "Why so serious?" He sticks the blade in my mouth... "Let's put a smile on that face!" And..." (and he cuts the guy's mouth)
There is also another mention of his father during the party when one guy standing up to him says "We're not intimidated by thugs like you!" and the Joker goes to him and say "You remind me of my father..." (grabs him, knife to his mouth) "I HATED my father!"