The officer responded to a residence in the Miami suburb of Davie around 4:15 pm and learned that Walton had been arguing with a woman, according to a police report.
The woman was five weeks pregnant, the report said, and told Walton on Sunday that the child was his.
"During the argument, Walton pushed (the woman) to the wall and hit her several times in the face and head. I noticed (the woman) having swelling in her left eye, "Officer Davy wrote in a report. The victim's name was redacted in the report.
Walton has been charged with aggravated assault on a pregnant woman, the report said. Walton remained in the Broward County Jail awaiting Wednesday's hearing to determine his bond status.
Walton's lawyer, Michael Gottlieb, said he spoke with his client on Tuesday. He told CNN: "I do not believe Mr Walton is guilty of the charges, as alleged."
In a statement, the dolphins said they were giving up on Walton.
"We were informed about police work earlier this morning in relation to Mark Walton," said Dolphins CEO Chris Greer. "We hold our players to a high standard and we take these things very seriously. We will have no further comment for now. "
The Cincinnati Bengals selected Walton, who played at the University of Miami, in the fourth round of the 2018 NFL Draft.
In the second arrest, drug and reckless driving charges were dropped on plea deal; Walton was given a six-month sentence on the weapons charge, which was transgressed and he served three weeks, Gottlieb said. Charges for the January and February incidents were also reduced, the lawyer said.
CNN cannot independently confirm the resolutions in the three cases.
He closed, thanking the Dolphins for the opportunity and vowed to "make the most of this chance as a person and player when I return."
CNN's Thisil Martin and Amanda Watts contributed to this report.