The packet of biscuits has passed its expiry date or The packet of biscuits has past its expiry date.
Or both sentences correct?
No.
The first is almost correct. The correct verb is "passed" but there is no such word as "expiry"!! Use "expiration" instead.
The word "past" can be used as a noun, an adjective, an adverb, or a preposition -- but not a verb!