I'm assuming you're not a native speaker? (I'm not) - "to cut a deal" is a fairly common idiom that means to reach and agreement.
The origin is hazy, of the theories I've seen I consider this the best one: "deal" means both "an agreement" and "to distribute cards in a card game". The dealer, in the latter sense, first cuts the card deck then deals the card. "Cut and deal" -> "cut a deal".
It could also be related to "cut a check", which comes from an era before perforated paper was widespread, when one would literally cut the check out of a book of checks.
"cuts ____ deals" is not and more closely resembles the removal of deals related to ____.