Bill Smith, 55, said the "red-mist" descended on the man when he told him customers with pets had to use different cars under company policy.
Mr Smith had been sent to a Stirling address to pick up a passenger.
Central Scotland Police said they were following a "positive line of inquiry" after the weekend incident.
Mr Smith, from Sauchie in Clackmannanshire, had picked up an elderly woman at the address before the man came out of the house and tried to get in the car with the dog.
"The red-mist descended and he started kicking and punching the taxi," he said.
"I tried to call headquarters for help, but couldn't get any signal so I decided to leave immediately before things got any worse."
'No respect' After the elderly woman left the car Mr Smith started his car engine, but the man allegedly opened the passenger door and threw in the pit bull.
Mr Smith said he was forced to jump out the driver's door, but was able to get back into the car when the man yanked back on the dog's lead.
He then drove off.
He added: "It's incredible what you put up with just trying to do your job offering a service to people.
"You treat people kindly and you expect that back, but it doesn't always work that way. There is no respect for your fellow man."