You may choose to draw cards to pay the cumulative upkeep cost even if the number of cards you’d have to draw exceeds the number of cards in your library. If enough of those draws are replaced by replacement effects so you don’t actually attempt to draw a card with an empty library, everything’s fine. However, if you do attempt to draw a card with an empty library this way, Psychic Vortex will remain on the battlefield but you’ll lose the game as a state-based action as soon as the cumulative upkeep ability finishes resolving.

Psychic Vortex’s cumulative upkeep ability has you draw cards as a cost. If you choose to do so, and some or all of those draws are replaced by replacement effects, you are still considered to have paid the cumulative upkeep cost.