Mashinter, 25, had three shots on goal and 10 penalty minutes in six games with the Rangers this season. In 11 games with the Rangers' American Hockey League affiliate, the Hartford Wolf Pack, he had seven points and a plus-3 rating.
The Blackhawks assigned Mashinter to their AHL team, the Rockford IceHogs.
Beach, 23, was taken by the Blackhawks with the 11th pick of the 2008 NHL Draft, but never made it to the NHL. He has four goals in seven games with Rockford, his sixth AHL season. The Rangers assigned Beach to their AHL team.