According to the Daily Star, the entertainer - who was hired to narrate the stage show - decided to ignore the script.
"Paul changed the script and refused to say certain lines," a source claimed. "He was a nightmare to work with in the end.
"The first 10 minutes of the play turned into The Paul O'Grady Show."
The insider added: "This is a huge production [and] it was decided that Paul should be replaced.
"He didn't take the news very well and decided to make a number of wild accusations."
The 56-year-old last week hit out at producers for postponing the shows, urging Reckless Entertainment to pay the cast and crew.
Bosses apologised to ticket holders after pushing back planned tour dates in Dublin, Belfast and Newcastle to improve the quality of the script.
Coronation Street actresses Kym Marsh and Katy Cavanagh are among the Street of Dreams cast.