Inspector Rob Lawton said he was "deeply saddened" by the incident and asked anyone with information or dashcam footage to come forward.
He added: "Whilst the vehicle is yet to be traced, we will of course review any new or further information provided to us."
Chris Hallam, 18, was left traumatised after he saw the lurcher thrown from an oncoming vehicle as he drove along the A52 in Radcliffe-on-Trent, Nottinghamshire.
He said he was travelling along the dual carriageway at around 2.45pm on Wednesday (20 October) when he saw something "flying through the air."
Mr Hallam got out of his vehicle and rushed over to the injured one-year-old dog as it lay in a pool of blood by the roadside.
He put the dog, called Ice, into the boot of his car and took it to Minster Vets in Nottingham, but his injuries were so severe he had to be put down.
Mr Hallam said: "It was just the most horrific thing I have ever seen, the poor thing didn’t stand a chance.
"I was driving along the road when I noticed something flying through the air as I passed an old farmer-type pick-up truck coming in the opposite direction.
"I pulled into a lay-by and ran over to help and two other guys who also stopped said they had seen a commotion in the back seat just as it happened.
"So we’re pretty sure it was deliberately thrown and just don’t understand how anyone could want to do that to a dog.”
"The noise coming from him was heartbreaking, he was in so much pain so I took him to the RSPCA at first.
"But they said they couldn’t do anything so I took him to a vets and they came out to my car and sedated him and put him on a stretcher.
"I went to work and my mum phoned me later on to say it hadn’t survived.”
‘Terrified and in a lot of pain’
The dog had suffered broken bones in his pelvis and internal injuries which vets couldn’t operate on.
A spokeswoman from the vets added: "He was just so terrified and in a lot of pain.
"We had to sedate him while in the back of the car before we could take him out to examine him, which is when the scans showed the problems of the internal injuries."