The male, with his pet carrier in his hands, can be seen caught between the pair, with one carrying what appears to be a machete.
Bystanders were left watching in horror from the safety of a nearby building as one of the men reportedly waved the large blade around in the car park on Tuesday morning.
Police were called to the scene in Plymouth at around 11am after reports of an altercation between two men. Officials said armed police made one arrest, while the second suspect was on the run.
They also confirmed a member of the public had been grabbed by one of the men, as another made threats with a weapon.
One woman said she saw the incident unfold after she arrived with her daughter to take their cat into the PDSA Animal Hospital.
The man was apparently used as a human shield as he was taking his pet to the vets
She said: "It was really scary. We arrived and these men were screaming and shouting at each other. I had to move my car in the car park because it was getting frightening. Spanners and metal bars were being thrown. It was going on for ages.
"Then one man went into the tree surgeon van and then ran across to the other man with a machete. It was just awful. We were locked into the PDSA hospital and I started filming, knowing the police needed the evidence.”
One of the two men drove off in a silver Ford Transit van which was later stopped by armed response officers and the driver arrested on suspicion of affray.
The second suspect involved in the incident, described by police as white, in his late 30s and balding, was last seen heading off on foot.
One of the men was carrying what appears to be a machete
We arrived and these men were screaming and shouting at each other
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Police added the man was wearing a green top with orange and yellow stripes and a yellow motif on the chest as well as blue trousers which were tucked into a pair of boots.
Travellers are said to have set up camp there at the weekend and a spokesman for the PDSA hospital said several caravans set up camp in the street beside the building on Saturday, along with a number of vans.
He said: "There are more people there than yesterday and they have lots of dogs running around. We've asked them to keep them tied up because they're running up to clients who are bringing in their sick and injured pets.
"It's possible their dogs are not fully treated for fleas and vaccinated and we have to consider the welfare of our client's animals. Our priority is the sick animals and if pets are being harassed and put under extra stress then it doesn't benefit their welfare.
"The travellers have been parking one of their cars on our land and they have made a couple of campfires on our land which we'll have to clear up. Being a charity we can ill afford that."