"Cut a deal" is an idiom, not slang: it's appropriate language to use in a business context, for example.
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.
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.