They are different sources of damage and cause separate death saving throw failures
This is because the piercing damage happens on a successful hit and the poison follows a saving throw - two separate mechanics so two separate sources of damage.
In contrast, a spell like Meteor Swarm is a single source despite doing two types of damage.
So, yes, unless the unconscious creature is immune to piercing or poison damage one critical hit from a wyvern will kill them if they are already at 0 HP.
