"Great suffering will have been caused, and purely for the sake of entertainment. Not only do these animals endure stress and fear every time they are forced to perform in the ring, they also risk injury and death."
SAFE has long campaigned for the rodeos to be banned.
"Events like these are nothing more than animal cruelty and have no place in a modern New Zealand."
Cocks said they operated under the Ministry for Primary Industries' code of welfare, but accidents could happen, as in any sport.
Carter also took aim was how bullride events were run - she said bulls were forced to wear a tight flank strap, cowboys' spurs "added to their torment" and investigators at New Zealand rodeo events had filmed bulls being riled up into performing.
This included shocks with electric prods, jabbing or kicking, and having dirt rubbed in their faces.
"Despite the reputation bulls have as powerful and aggressive, they are simply prey animals fighting for their lives. They don't know that this is being done just for 'fun'."
Protests had taken place outside the bullride last night, matching anti-rodeo pickets at other events. Sixty-two-thousands people had also signed a petition last year calling for a rodeo ban, Carter said.
Cocks said the flank rope criticised by SAFE was padded with sheepskin, as is required in New Zealand, and firm, but not tight.
"It's nothing more than a piece of harness ... so the bull knows it's time to compete. Contract bulls are used to this."
He did not know if the dead bull was a contract bull.
There were strict national guidelines about the use of spurs, which were followed, he said.
Cocks also called allegations bulls were riled up into performing "totally false".
"These animals are very expensive, well cared for, healthy ... why would we do that do animals we cherish?"
The organisation might have captured footage of mistreatment "years ago", but the sport had evolved since then, he said.