I think the word you are half-remembering is punitive - inflicting or intended to inflict punishment; retributive, punishing (OED).
Note, however, that punitive means 'punishing' and not 'disproportionately punishing'. Even when used in law (as in punitive damages) the sense is that punitive damages compensate the wronged party and also punish (within reasonable bounds of proportionality!) the wrong-doer.
To have the sense sought by the OP you would need to say something like excessively punitive.
Setting aside the OP's request for a word beginning with 'P', draconian seems like the best fit for the sense described.