The main characters in this story include the Colonial Policeman, and the crowd, and, of course, the elephant.
The Colonial Policeman is British, a member of the governing body that controls Burma. This Policeman is despised by the people he is sworn to protect. He, himself, has a difficult time dealing with the insults and taunts of the people. He doesn't like the imperialism that his country has imposed on these people. He sympathizes with them, but his behavior must conform to certain standards. Therefore, when he is called to respond to a rampaging elephant at the market, he is expected to shoot the animal dead.
When the Policeman arrives too late to stop the elephant from destroying parts of the market and killing a man, a slave, he has a difficult decision to make, whether he should shoot the elephant anyway or find the mahoot, the master of the elephant and have it taken away from the market. The elephant is a working elephant, very valuable, who has slipped his chain and wandered away from his master.
The elephant is now grazing, quietly, no longer dangerous, but calm. The elephant must be dealt with, the crowd demands it.
The crowd that is gathered has a degree of antagonism toward the Policeman, taunting him, jeering at him, disrespecting his position, hating him for being a representative of the imperial government that rules their country.
They are rabid with desire for the death of the elephant. They demand that the policeman kill the elephant. He does not want to harm the elephant. But, he must satisfy the crowd, for two reasons, first the elephant did kill a man, and because if he doesn't kill the elephant, the crowd will never respect him in any way. He has no choice but to please the angry raging mob. He shoots the elephant and the crowd seizes the moment tearing the flesh off the dead elephant's bones like a crazed bunch of savages.
Orwell makes a distinction here, the elephant was less violent that the crowd, the Policeman, the imperialist, does not want to kill the elephant, the crowd, the natives are savage in their thirst for blood. It appears that the crowd is the source of violence and cruelty in this story, not the elephant or the policeman.