The footage then showed a man arriving at the tractor and dragging the cow along the ground with the tractor.
In a statement, the organisations said the conviction sent a message that cruel treatment of animals will not be tolerated.
It is a step in the right direction, but more still needs to be done to prevent cruelty happening.
"We are pleased to see the Ministry for Primary Industries (MPI) taking these cruelty cases seriously," said Farmwatch spokesman John Darroch.
"However, prosecutions only go so far and act as a minimal deterrent. More time, effort and funds need to be put into preventing cruelty to vulnerable animals in the first place."
According to the organisation's statement, the farmer was convicted, fined and ordered to pay costs towards the prosecution.
The use of hip clamps to support a cow that is unable to stand is legal, but the treatment of the cow in this case was found to contravene the law.
Farmwatch had also previously released footage showing apparent mistreatment of bobby calves.
Two workers at Down Cow Ltd slaughterhouse were charged for severe mistreatment of calves.
Last May, a farmer was convicted of cruelty for dragging a newborn calf by the hind leg along the ground for 40 metres.
"It should not be up to volunteers and non-profits to expose issues of animal cruelty," said SAFE campaigns director Mandy Carter. "SAFE is concerned that there are likely many more animals suffering."
SAFE is urging the new Government to have an independent animal welfare body, separate to MPI, to monitor and enforce animal welfare.