Hamsters can indeed kill each other when they fight. Hamsters are solitary animals with a strong sense of territory. When they sense that they are under threat, they will initiate fights to compete for territory and food. Whether they are same-sex or opposite-sex hamsters, fierce battles may occur until there is only one hamster left in the cage.

Reasons for Hamsters' Fights
Conflict during the Mating Season: During the mating season, male hamsters become extremely irritable in order to compete for the right to mate and are likely to conflict with other hamsters.
Territory Dispute: Hamsters have a strong sense of territory, and same-sex hamsters are prone to fighting over territorial issues.
Temperament Changes during Pregnancy: After a female hamster gets pregnant, her temperament may become irritable, making her likely to conflict with other hamsters.
Methods to Avoid Hamsters' Fights
One Hamster per Cage: The safest way is to keep each hamster in a separate cage, which fundamentally eliminates the possibility of them killing each other in a fight.
Separate Them in Time: During the mating season or pregnancy, arrange a single room for the hamster to avoid unnecessary conflicts.
Avoid Keeping Same-Sex Hamsters in the Same Cage: It is easy for same-sex hamsters to fight when they are kept together, so it is safer to keep them separately.
Provide Sufficient Toys and Food: Ensure that they have enough entertainment facilities and food to reduce conflicts caused by hunger or boredom.
Measures for Handling Injuries
Examine the Wound Carefully: After finding that a hamster is injured in a fight, first carefully check the severity of the wound. Minor injuries can be treated at home, while severe wounds or continuous bleeding require immediate medical attention.
Clean and Disinfect: Wash the wound with normal saline, apply iodophor for disinfection, and finally apply a little aureomycin eye ointment. Minor wounds will heal quickly.
Seek Medical Help in Severe Cases: If the wound is severe or bleeding persists, stop the bleeding, disinfect, and bandage it immediately, and then take the hamster to a pet hospital for treatment.