Actually the script says:
'OBI-WAN uses the Force to catch his lightsaber and he tosses it to ANAKIN. With TWO LIGHTSABERS, ANAKIN attacks. COUNT DOOKU parries and ripostes. It is no contest. ANAKIN is driven back against the wall. He loses one lightsaber. Finally COUNT DOOKU, in one flashing move, sends Anakin's arm, cut at the elbow, flying still gripping his lightsaber. ANAKIN drops to the ground in agony. COUNT DOOKU draws himself up to deliver the coup de grace.'
The novel does suggest a tough fight though and in the movie he is out of breath after the duel. Novel:
'For the first time, Count Dooku lost his little confident smile. He had to work furiously to keep Anakin's blade at bay, dodging more than parrying. He tried to step out to the side, but stopped as if he had hit a wall, and his eyes widened a bit when he realized that this young Padawan, in the midst of that assault, had used the Force to block his exit.
"You have unusual powers, young Padawan," he sincerely congratulated. His little grin returned, and gradually Dooku put himself back on even footing with Anakin, trading thrust for slash and forcing Anakin to dodge and parry as often as he tried to strike.
"Unusual," Dooku said again. "But not enough to save you this time!" He came on hard, thinking to drive Anakin back and off balance as he had driven Obi-Wan back. But Anakin held his ground stubbornly, his green blade flashing left, right, and down so forcefully and precisely that none of Dooku's attacks got through.
Off to the side, Obi-Wan understood that it couldn't hold. Anakin was expending many times the energy of the efficient Dooku, and as soon as he tired...
Obi-Wan knew that he had to do something. He tried to come forward, but winced and fell back, in too much pain. As he collected his thoughts, he reached out with the Force instead, grabbing at his lightsaber and pulling it in to his grasp. "Anakin!" he called, and he tossed the young Padawan the blade. Anakin caught it without ever breaking the flow of his fighting, turning it under and igniting it immediately, putting it into the swirling flow.
Obi-Wan wat ched in admiration as Anakin worked the two blades in perfect harmony, spinning them over and about with blinding speed and precision.
And he watched with similar feelings the working of Count Dooku's red lightsaber, flashing ahead and back with equal precision, picking off attack after attack and even countering once or twice to interrupt the flow of Anakin's barrage.
Obi-Wan's heart leapt in hope as Anakin charged forward suddenly, bringing his green blade over his shoulder and across, down at the Count. Obi-Wan understood immediately, even before he noted Anakin's blue blade coming up and over the other way-the green blade would push the Count's lightsaber out of the way, clearing the path for the victorious strike!
But Dooku retracted impossibly fast, and Anakin's down-cutting green blade hit nothing but air.
Dooku stabbed straight ahead, intercepting the blue blade. The Count's hand worked up inside and over, then back around with a sudden twist, launching the blue lightsaber from Anakin's grasp. Dooku went on the offensive immediately, driving the surprised and off-balance Anakin back.
Anakin fought hard to regain his fighting posture, but Dooku was relentless, thrusting repeatedly, keeping the young Padawan stumbling backward. And then he stopped, suddenly, and almost on reflex, Anakin turned back on him, roaring and slashing hard.
"No!" Obi-Wan cried.
Dooku stabbed ahead and slashed out suddenly, intercepting not Anakin's green blade, but the Padawan's arm, at the elbow. Half of Anakin's arm flew to the side, his hand still gripping the lightsaber.
Anakin dropped to the ground, grabbing his severed arm in agony.'