Here's a breakdown of why:
* Previous Injuries: He's already sustained injuries from his battle with the Careers, including a spear wound to his leg and a broken arm.
* The Muttations: He's been relentlessly attacked by the genetically engineered "muttations" created by the Capitol. These attacks have further weakened him.
* Exhaustion: The games have been physically and emotionally draining. Cato is tired and his fighting spirit has been broken.
By the time he reaches the final showdown, Cato is practically defenseless. He's too injured to use his sword effectively.
The lack of a weapon in his final moments highlights his desperation and the brutality of the games. He's reduced to a vulnerable creature, struggling to survive against a resourceful and determined Katniss.