Police believed a crossbow was used to kill the calves and injure another between 10.30am and 5pm on June 19.
They were part of a herd of 220 calves, owned by a Southland dairy farmer, being reared near Dunedin.
The herd was grazing a paddock along Coast Rd at Seacliff, north of the city.
Constable Jon-Paul Tremain, of Waikouaiti, said one calf was butchered by the alleged poachers, who took everything but the animal's internal organs.
Another had its head cut off and the carcass was left in the paddock, and a third died a slow painful death when shot in the stomach with a crossbow.
Of the three calves killed, one was a family pet which had been hand-reared.
Another was found alive with crossbow bolts stuck in its ear and neck.
Bolts and a bag containing arrowheads were recovered from the paddock and forensically tested. The calves' DNA was also tested.
Const Tremain said the calves' owner posted a reward of $5000 for any information which led to the successful prosecution of those responsible.
Each calf was worth between $900 and $1600, at local and export prices.
The animals would have joined a dairy herd once mature.
Anyone with information about the incident is urged to contact Const Tremain on (03) 465-9127 or Crimestoppers on 0800 555-111.
