"Perchance to Dream", a short story by Sally A. Sellers; first published in Isaac Asimov's Science Fiction Magazine, Spring 1977, available at the Internet Archive.
Years ago I read a short story about a woman trying to commit suicide. However, because she had a extremely high rate of healing, her wounds were never fatal.
After he returned home, his body forced him to sleep, but his dreams allowed him no rest. He kept seeing a lovely young woman, with three moles on her cheek—a weeping, haunted, frantic woman who cut herself again and again and thrust the mutilated arm before his face for him to watch in amazement as the wounds closed, bonded and healed to smoothness before his eyes. In minutes.
God, if she would only stop crying, stop pleading with him, stop begging him to find a way to make her die—to use his medical knowledge somehow, in some manner that would end it for her. She wanted to die. She hated herself, hated the body that imprisoned her.
The story ends with her being in the morgue after her heart was taken out for transplantation.
Two men lifted the casket and bore it outside in the rain toward the oven.
Cells divided, differentiated, and divided again. The reconstruction was almost complete. It had taken a long time, almost twenty-four hours. The body had never been challenged to capacity before. Removal of the major organs had caused much difficulty, but regeneration had begun almost at once, and the new tissues were now starting the first stirrings of renewed activity.
Before a new heart could grow she was incinerated.
There was a shadow of awareness for a long moment, and then it was gone.
After thirty minutes, the oven temperature was nine hundred degrees Fahrenheit. The thing on the table was a third of its original size. The secondary burners flamed on. In another half hour, the temperature had reached two thousand degrees, and it would stay there for another ninety minutes.
The ashes, larger than usual, had to be mashed in a chalky, brittle dust.
The person who received her heart received the quick healing as well.
The girl spoke up in a high voice. "Is my new heart okay?"
"It's fine, honey," said Dr. Kornbluth. Then she lowered her voice. "This is physiologically impossible! The incision has completely healed, without scar tissue. And in thirty-two hours, doctor? In thirty-two hours?"