Probably you're thinking of this passage from Part 3, Chapter 3 (emphasis added):
Winston was struck, as he had been struck before, by the tiredness of O’Brien’s face. It was strong and fleshy and brutal, it was full of intelligence and a sort of controlled passion before which he felt himself helpless; but it was tired. There were pouches under the eyes, the skin sagged from the cheekbones. O’Brien leaned over him, deliberately bringing the worn face nearer.
‘You are thinking,’ he said, ‘that my face is old and tired. You are thinking that I talk of power, and yet I am not even able to prevent the decay of my own body. Can you not understand, Winston, that the individual is only a cell? The weariness of the cell is the vigour of the organism. Do you die when you cut your fingernails?’
He turned away from the bed and began strolling up and down again, one hand in his pocket.
‘We are the priests of power,’ he said. ‘God is power. But at present power is only a word so far as you are concerned. It is time for you to gather some idea of what power means. The first thing you must realize is that power is collective. The individual only has power in so far as he ceases to be an individual. You know the Party slogan: “Freedom is Slavery”. Has it ever occurred to you that it is reversible? Slavery is freedom. Alone — free — the human being is always defeated. It must be so, because every human being is doomed to die, which is the greatest of all failures. But if he can make complete, utter submission, if he can escape from his identity, if he can merge himself in the Party so that he IS the Party, then he is all-powerful and immortal. The second thing for you to realize is that power is power over human beings. Over the body — but, above all, over the mind. Power over matter — external reality, as you would call it — is not important. Already our control over matter is absolute.’
I didn't go to check Youtube to find a video with a timestamp, but the entire text of Nineteen Eighty-Four is available online from Project Gutenberg Australia, so I just needed to Ctrl+F for "mortal" in each chapter of Part 3 in turn. Here's the relevant chapter so you can read it in full.