There's no indication that Rey chopped Ren's hand off.
He was up again in an instant, but not in time to fully deflect a
following blow from Rey’s weapon. He succeeded in blocking it, but he
still took the full force of the strike against the haft of his own
lightsaber. The weapon went flying into the snow. Unarmed, he raised a
hand and utilized the Force to fend off one slashing blow after
another, until finally her fury penetrated his remaining defenses.
Taking a glancing blow to the head and chest, he went down, a
prominent burn slashed across his face. Weakened, he reached out
toward his lightsaber, trying to draw it to him.
Star Wars: The Force Awakens - Official Novelisation
Staggering back to his feet, his parry could not match the strength of
her swing. It cast his lightsaber out of his grasp.
Ren extended a hand, calling on the Force to ward off her attacks. At
first it worked, as she slashed into the iron shield of his will, but
then her blade cut across his face. It burned.
He looked up at the girl whose lightsaber hovered over his chest. He
shivered under the coldness of her stare. He who had been so eager to
kill was not eager to die. Kylo Ren was afraid.
The girl withdrew from him.
Star Wars: The Force Awakens - Junior Novelisation
She intensified her attacks, sensing more than seeing where he would
strike next. Her blade cut across Kylo’s face before connecting with
his saber hilt. Kylo’s weapon went flying into the snow.
Rey stood above him with her lightsaber raised. He was defenseless.
She could strike him down right then and end it all.
The Force Awakens: Rey's Story
Nor the script
Rey closes her eyes for a long beat. When Rey opens them, she is
centered, fortified, and she POUNDS BACK, SINGLE HANDED SWIPES,
hitting Ren's gnarly, spitting saber with incredible FORCE. It's so
fast now, so furious, that Kylo Ren FALLS BACK -- She ATTACKS HARDER!
Ren gets up again but she HITS HIS SABER'S HILT -- HIS BLADE GOES
FLYING OFF, TUMBLING INTO THE SNOW -- and she SLASHES AGAIN AND AGAIN
AND HITS KYLO REN SQUARE IN THE HEAD AND CHEST. HE GOES DOWN, SUDDENLY
A FEARFUL MAN, A LARGE BURN SCAR SLASHED ACROSS HIS FACE! He still
reaches for his saber. And she could kill him -- right now, with ONE
But she stops.
Also, y'know, counting skills