The "crippled youngster" from District 10 was a tribute who finished in the top 12. Peeta's limb was amputated owing to serious injuries and blood loss. Mention is made of peacekeepers shooting a youngster who "wasn't right" (most likely developmentally delayed) because he kept night-vision goggles to play with. This is probably why Peeta got his leg amputated: to prevent him from being killed or injured during peacekeeping operations.
In addition, it is possible that they just wanted to stop the bleeding. The amputation was apparently performed by a surgeon using a laser beam called a "coagulator".
Peeta later wins the game with his graciousness and displays an unusual level of selflessness by volunteering for Cato's role as tributes leader. This earns him some points with Katniss and shows how much he has changed since first arriving in Capitol territory. He also manages to convince the other contestants that killing children is wrong even though they are playing for their lives. In the end, it is Peeta who saves Katniss's life when she is taken hostage. He then sacrifices himself to save her yet again at the final moment of the game. Although this does not win him any points with Katniss, it does show how much she cares about him despite everything that has happened between them.
It is possible that they had no choice but to remove his leg.
Amputation of Peeta's Leg You wouldn't have suspected it based on how the movies depicted it. However, Peeta's injuries was even severe than you suspected. The Capitol declared his limb unsellable, chopped it off, and replaced it with an artificial one since it was so terrible.
His family was given permission to visit him in prison, but only one of them could stay with him at a time because they thought that he needed rest more than food. But really it was just so they could drink their champagne without being caught by the guards. During one of these visits, before they were arrested by Peacekeepers, he told Katniss that if she survived the Hunger Games, she should meet him at the end of the arena. If she did, he would give her a secret message for her sister.
After the death of his family, he was taken to another room and left alone so he could think about what had happened. Then President Snow came in and told him that since he was no longer useful, he could be released. After that, we don't see him anymore until the start of the 74th Hunger Games.
In the movie, his leg is shown being chopped off by an ax. In reality, it was a circular saw that cut away most of his leg up to the knee.
He has "wide shoulders and a robust build." Following the 74th Hunger Games, a portion of Peeta's left leg was severed, requiring him to walk with the assistance of a prosthetic limb for the remainder of his life. His leg is never amputated in the 2012 film adaption.
In addition to his physical disability, Peeta also struggles with post-traumatic stress disorder as a result of the events of the Games. He becomes obsessed with maintaining an ideal image of himself through social media, which creates problems for his relationship with Katniss.
Although he does not mention it by name, it is possible that Peeta wears a prosthetic leg due to having been born without fibulae (leg bones). This would explain how he was able to win the Games after being shot in both legs.
In reality, Peeta's leg is completely fake. It was added to his body in a special effects workshop so that he would not have to wear pants during filming.