Mr Cochrane and his father jumped in their boat and quickly found the orca several hundred metres offshore between Hahei and Hot Water Beach in water that was about 25m deep.
"We saw the buoy first, then splashing in the water.
"It was just coming up to the surface for air ... It looked pretty sad. I'd say it was pretty buggered from what it had been through."
Mr Cochrane believes the cray pot was on the bottom of the ocean, forcing the 4m-long orca to drag it to the surface each time it needed to come up for air. The orca appeared pretty calm, despite having visible injuries on its head, tail and body - and being very vocal.
"It would have definitely hurt him ... There were rope marks [on its head] and around its body and the tail. The rope was cutting quite far into its flesh."
Mr Cochrane said he dived under the surface to investigate with a video camera before going back down to remove the rope, while the orca's mates looked on.
"I was trying to cut it off then the pod came around and I got a little bit scared but then I just went back down, grabbed on to its tail and wrapped my legs around the rope and cut it off."
He said the rope came off quickly but it took the slightly stunned orca a few seconds to realise it was free again.
"He kinda sat there for five or 10 seconds then swam away pretty quickly."
Russ Cochrane said he was not concerned about his son's safety and described the experience as "once in a lifetime".
He said footage they recorded and posted online yesterday had resulted in calls from journalists from as far away as America who wanted to know more about the rescue.