>>36130242I imagine Pokémon as having some kind of particular "skin" or molecules or even a force field (HP) around their body that deflects more or less other Pokémon's attacks (implied to be charged with the PP energy), and that's what the trainer relies on for battling, or fights for dominance between Pokémon themselves.
However, cutting a Pokémon, biting it, eating it, crushing it by any other mean not related to the HP/PP dynamic injures them just as much as any other animal, their personal physical defences (made of steel, rock, covered in poison or close to water in composition etc.) being able to deflect the damage or not.
Some Pokémon would have interesting causes of death, eg. Vaporeon would pretty much evaporate, and dissipate so much into the stratosphere its molecules would never reform.
I also guess a Pokémon left to struggle for too long without PP would actually die.