This is "The Extra" by Greg Egan.
The story is about a rich man who makes clones of himself. The clones are fed and exercised so that they will have perfect bodies, but are not given the ability to mentally develop.
Keeping a stock of congenitally brain-damaged clones of oneself - in the short term, as organ donors; in the long term (once the techniques were perfected), as the recipients of brain transplants - was not illegal, but nor was it widely accepted. [...] There had been legal challenges, of course, but time and again the highest courts had ruled that Extras were not human beings. Too much cortex was missing; if Extras deserved human rights, so did half the mammalian species on the planet. With a patient, skilled trainer, Extras could learn to run in circles, and to perform the simple, repetitive exercises that kept their muscles in good tone, but that was about the limit.
When the rich man gets old, he switches his brain into one of the clones. This way, he will give himself a new, fresh body. However, he is horrified to find that when he wakes up after the transplant, he is in the same body.
When, at last, one arm came under his control, he raised it, with great effort, into his field of view.
It was his arm, his old arm - not the Extra's.
He tried to emit a wail of despair, but nothing came out.
Something must have gone wrong, late in the operation, forcing them to cancel the transplant after they had cut up his brain.
He has transplanted his brain, but not his soul, or his memories.
Of course he was dreaming. What other explanation could there be?
Unless the transplant had gone ahead, after all.
Unless the remnants of his brain in this body retained enough of his memory and personality to make him believe that he, too, was Daniel Gray. Unless the brain function studies that had localised identity had been correct, but incomplete - unless the processes that constituted human self-awareness were redundantly duplicated in the most primitive parts of the brain.
In which case, there were now two Daniel Grays.
He tries to tell the operators that there has been a mistake, but he finds himself unable to get the words out. he realizes he will be trapped as an idiot forever, while the clone steals his life from him.
He had given up trying to communicate his plight to the people around him. He knew he would never master speech, and he couldn't even manage to convey meaning in his gestures - the necessary modes of thought were simply no longer available to him, and he could no more plan and execute a simple piece of mime than he could solve the latest problems in grand unified field theory.