At the very beginning before they fight in the first level Scorpion says "You will fail." and "I will win." before they fight.
After you defeat him he mumbles something like "Wait," "Please," or "No." before you kill him.

Later they encounter each other in the Prison of Souls and this is the cincema scene before they fight:

"Captured and now imprisoned, Sub-Zero peers out of the bars of his cell and ponders his escape. He fails to notice the shadowy figure of a warrior behind him.

Warrior: Escape is not possible.

Sub-Zero: Who are you?

Warrior: I am a dead man. But somehow you have retained your mortality, which would mean you are vulnerable to death.

Sub-Zero: Wait... I know your voice.

Scorpion: Yessss... I am Scorpion. You killed me in cold blood.

Sub-Zero: I had no choice. If I had not stolen that map I would be the dead one.

Scorpion: But my clan and family would still be alive!

Sub-Zero: What??

Scorpion: It wasn't enough to kill me...you had to destroy every last remnant of my being...you are responsible for the massacre of my entire clan!

Sub-Zero: You're mistaken... Quan Chi is responsible for their deaths!

Scorpion: Words will not save you Lin Kuei warrior... prepare for your final battle!"

That's the only dialogue they exhange in the actual game.

Thanks. Is there any dialogue after you beat Scorpion the second time? Or after you knock Scorpion out does Sub-Zero just run out the door?

No they dont talk after you beat him the second time. Scorpion just falls to the ground and disappears and then Sub-Zero just runs out of the door.