Does anyone remember an old black and white movie (or maybe all I had at the time was a black and white television) where two men were pretending to be magicians and were about to do the saw the lady in half trick. One of the men says, “With my luck I’ll get the half that talks.” That’s about all I remember. I thought they did a pretty good job of getting stuff past the censor.
I’m not sure I see why that would/should have been censored. Do you mean because of the sexism? (damn mouthy wimmins!)
What would the other half be capable of doing?
Googling that line produces
The reference is found below
I think the part where she says: “Go ahead, rip me in two” is more suggestive than the “half that talks” line.
Woody Allen used a similar line in a scene with Diane Keaton in Love and Death.
She is talking about her sensuality and spirituality and says, “I guess you could say I’m half saint, half whore.”
He replies, “Here’s hoping I get the half that eats.”
I don’t think Agony is where I heard it. It looked more like a 40s or 50s movie. The lady that was the subject of the line was a magician’s assistant already in the box for the trick. I don’t recall anything other than American accents.
Was the scene in Agony anything like this? I don’t remember ever watching Agony.
I may not be getting the line exactly correct. Maybe the line was, “With my luck I’ll get the end that eats and talks.” or some other variation. I have had no luck with Google with any of this.
I recognize it as a Benny Hill joke, which by definition means it was stolen from some long dead vaudevillian.
I think the point was that the other half didn’t talk. Absence of talking was the desired trait.
It was immediately clear to me that the joke was that the other half included the genitalia. I think this might be an old joke that has been recycled many times.
As seen in one of Piet Hein’s Grooks:
The Little Mermaid’s Little Sister
was also partly girl and cod
though in a way which those who kissed her
found odd.…but which, well worth to mention,
though at first sight absurd,
I, with my fond intention,
preferred.
Why can’t it be both? 
The point being there’d be a win-win half and a lose-lose half.
But I’m with @Ynnad here. The obvious interpretation is what @Darren_Garrison points out. But it’s the unstated second half of the equation that contains all the punch.
In our modern full-frontal-everything world it’s easy to forget just how refined was the art of the double or triple entendre. One of my favorite examples from the 1960s was from a Tom Lehrer album recorded live in a large theater with a large crowd. He’s doing a monologue intro to a song and says
Harry used to major in Animal Husbandry. Until they caught him at it one day.
A small fraction of the audience begin to titter and laugh and you can hear this slowly filtering around the room without building to a crescendo. At which point Tom cuts off the moment by saying:
The rest of you can have it explained to you when you get home.
And begins playing whatever song was being introduced.
All the humor there needs to be worked for; it isn’t obvious. Unlike in our modern unsubtle zero-attention-span era.
I kinda feel like I saw this in a movie recently. One old movie I watched this summer was “Yankee Doodle Dandy.” Perhaps it was said by a magician during George’s vaudeville days?