Why does Smiley burn the photo/negative?

Why would anyone want it? It's got too many bloodstains on it for anyone's liking and they already have enough evidence to turn both Grigoriev and Karla.

I can't think of a valid reason to burn the negative, either.

He didn't just throw it away, rip it up or flush it down the toilet. He took the trouble of burning it up to make sure it was destroyed. So it's not just that the negative wasn't necessay any more, it actually had to be destroyed, I guess.

However, keep in mind that Le Carre wasn't an ordinary writer who conjured stuff up to make suspense or drama. He did serve in the secret service and base his novels on his experiences. That's why his works feel so realistic. Particularly concerning his main character Smiley, everything he did or said had a purpose. Just because you or I can't figure it out doesn't mean it's pointless or idiotic. There's probably an explanation in the book, which I haven't read yet.

Edit:

Perhaps it was out of respect to Otto. It may be that Smiley did not want a naked foursome picture to be the last thing left from him. Smiley wasn't exactly sentimental, but he did respect certain people.

Never be complete.

I think that's correct. Also, that negative had been the cause of several deaths and so Smiley probably didn't want it languishing in the Circus archives. The point someone made above about it preventing salacious viewing is also right. And finally I think there may have been something about its destruction helping to protect Claus Kretzschmar and his lovely family, and also Mme Ostrakova. It was a dramatic moment for the screen which, as you say, wasn't in the book.