Fellow passenger Krista Rosolino, who recorded the video, described the incident in an open letter published to a blog.
She said Hamilton got out of his seat to quickly use the bathroom as the plane sat on the runway.
She said he was told that he couldn't use the bathroom the first time he asked to go. After waiting 30 minutes, Hamilton said it was an emergency and went to the restroom, according to Rosolino.
When he returned to his seat, however, a Delta employee told him to exit the plane.
"I need more information, sir," Hamilton is heard saying in the video. "I haven't done anything. I paid for this ticket, and ... I have to be home."
"I tried to hold it the first time, and you said I absolutely couldn't, and I'm being kicked off the plane?" he says. The employee responds, "I need to talk to you outside."
Hamilton said later that the plane was delayed in taking off and he could no longer wait to use the bathroom.
"Sometime later, we were still taxied, [and] the plane hadn't moved ... and it's at an emergency stage now," Hamilton told ABC affiliate WISN on Wednesday.
Describing Hamilton as a "nice gentleman" who played hide-and-seek with her infant as they waited to take off, Rosolino called the incident "the most outrageous treatment of a paying customer that I have seen."
She said the flight crew made all the other passengers get off the plane and reboard after the incident.
"Not only did your staff truly harm and humiliate one person who was forced to pay hundreds of dollars for a new same-day flight, but you forced the rest of us passengers to endure a 2 hour saga of watching a man being targeted for having a bathroom emergency," she wrote.
He said that he was forced to buy a ticket on another airline at three times the price to get back to Milwaukee.
Hamilton, who is black, told ABC News he was concerned his race may have been a factor, adding that he has not retained an attorney but is keeping his legal options open.
Over email, a Delta spokesperson said that Hamilton was removed from the plane because he did not comply with instructions.
In an accompanying statement sent by the spokesperson, Delta said it was important for passengers to comply with crew members' instructions.
"Our flight crews are extensively trained to ensure the safety and security of all customers," the statement read. "It is imperative that passengers comply with crew instructions during all phases of flight, especially at the critical points of takeoff and landing."