The purpose of a vapor barrier is to prevent moisture from condensing in the insulation, greatly reducing it's insulating value. To do this, it must be placed on the warm side of the insulation. In cold and moderate climates, this is towards the living space. In hot humid climates where keeping the living area cool is the primary concern, it goes towards the weayther side.
It sounds like in your case the paper is on the top, weather side. If you are in a hot humid climate and you are adding more insulation on top, you WANT to have many holes in the old barrier that is now sandwiched inside all the insulation, allowing any moisture that got past the new barrier on top to hopefully get carried out without condensing.
If you are in a cold or moderate climate, and it is on top, it was installed wrong. You're better off having holes in it. Any moisture that got that far should be allowed to escape, lest it condense on the paper and make the insulation wet.
To summarize, in either climate, if the paper is on top of the old, and you are adding more insulation, put all the holes in it you can! It is not helping. In a hot humid climate, insure you place a new barrier on top of your new insulation. If you are in a cold or moderate climate, consider how you may add a vapor barrier to the living space. Several heavy coats of latex paint can do this. It may be something you already have.