The only such monster is the demilich
The demilich has a number of damage immunities including from nonmagic bludgeoning, piercing, and slashing. It also has resistance against magic piercing, slashing, and bludgeoning.
There are only few monsters in the monster manual that have immunity or resistance to a single one of the three damage types and none of ...
The demilich fits your criteria:
Damage Resistances Bludgeoning, Piercing, and Slashing from Magic Weapons
Damage Immunities Necrotic, Poison, Psychic; Bludgeoning, Piercing, and Slashing from Nonmagical Attacks