The incident occurred with 1:52 remaining in the first quarter of Milwaukee's 112-104 loss to the Pelicans on Friday. Mayo got tied up with Stiemsma as he tried to get around a screen set by the big man.
"Certainly we don't want to respond the way O.J. did," Milwaukee coach Larry Drew said before his team played the Washington Wizards. "We want to be a little more under control."
Mayo was assessed a flagrant foul 2 and ejected.
It was the second consecutive game the Bucks, who have the worst record in the NBA, had a player miss a game for punching an opponent. Forward Ersan Ilyasova missed Friday night's 112-104 loss at New Orleans for punching Sacramento's Reggie Evans in the stomach on Wednesday night.
"Two unfortunate suspensions," Drew said. "If you are around this thing long enough, you will experience things that just seem to happen in the NBA.
"Emotions get high, and both incidents were two isolated incidents," he said. "It's just from being competitive, and in Ersan Ilyasova's case, playing against a physical guy."
Drew said guard Tony Mitchell, signed to a 10-day contract on Tuesday, might get extra playing time against the Wizards.