We know what the damage type of a crushing force is in 5E, though. It's bludgeoning. That's why the grasping hand effect of Bigby's hand does bludgeoning, as does any constricting attack from the likes of giant snakes.
High-pressure fluid jets can cut through things if sufficiently narrow and fast, but at that point you're still just looking at piercing or slashing. The injury isn't different to being poked with a sharp stick other than that you are also wet now. If it's not enough to cut with... well that's bludgeoning again