The short story was part of an anthology. A cancer clinic near a war zone receives a famous cancer patient who they attempt to cure. At the end they find a cure, but the cancer patient reveals he doesn't want to be cured. He instead wants to destroy any cures as he is nothing but a human-shaped tumor. According to him, cancer is the next phase in human evolution. He transforms into a bomb and blows up the clinic (the better to hide the evidence in the war zone), reforms to his original shape and walks off.
Edna Mayne Hull (aka Mrs. A. E. van Vogt), "The Patient".
The short story was part of an anthology.
The ISFDB bibliography page for that story has a list of anthologies and collections in which it appeared.
A cancer clinic near a war zone
London, Aug. 23, 1943--Reports reaching this capital state that a universal cancer cure has been perfected at the Midland-West Coast Hospital for Cancer Patients. Since the war, this hospital has been largely converted to military purposes, but one wing is still under the charge of the brilliant cancer research scientist, Dr. Lyall Brett, who is to make a public statement shortly.
receives a famous cancer patient who they attempt to cure.
"Remember my telling you of a patient who came to Carl Hamber's New York Cancer Institute last year--the fellow who'd been to every cancer institute as well as to every quack in the world? He's the perpetual cancer patient. He has an operation practically every year. They've cut cancer out of his throat, his chest, his head--and he's still alive. He's the cancer patient, known all over the world. If you can cure him--"
At the end they find a cure, but the cancer patient reveals he doesn't want to be cured. He instead wants to destroy any cures as he is nothing but a human-shaped tumor. According to him, cancer is the next phase in human evolution.
Brett sighed and said: "Why do you want to kill me? On the entire earth, I am probably the only man who can make you well."
The stranger shook his head. In the half-light, his eyes gleamed. "I am not a madman, Dr. Brett; and unfortunately for you, the very extent of your success makes it necessary for me to kill you. Let me ask you a question: Can you imagine a perfect physical being?"
It struck Brett sharply that if only he could keep the fellow talking . . . He said cautiously: "Universal adaptation would be a required ability for such a being. That means . . . amorphism . . . changing shape at will . . . which would require radical cell and tissue growth like--"
He stopped, his eyes wide. Before he could speak, the man Grainger said softly: "Yes, Dr. Brett, like cancer; and you would destroy the free-growth potentiality of the cell, man's hope for biological perfection, for adaptive power so complete that he can swim and fly and live in airless space, live anywhere under any conditions."
He transforms into a bomb
His mind wrenched from its hopeless thought. For the man was changing. Changing. His face was transforming, shining. Abruptly, there was a glistening steel-like bomb standing upended on the floor.
and blows up the clinic (the better to hide the evidence in the war zone),
The world ended in a shattering violence of explosion.
reforms to his original shape and walks off.
It took an hour for the dynamic cells of the man, in their blind will to cohesion, to come together. Slowly, in the darkness, Peter Grainger took form. He stood for a while, staring at the wreckage of the hospital wing; then he turned off into the night.