Other options - add a skim more concrete and re-grading the slope so it drains properly.
It doesn't have to be thick, but the concrete means there's no way for mud to form under the deck, or for weeds to grow.
Overall cost is probably about the same between disposal of old pad and a couple bags of concrete.
Either way you'll have to lift most/all of the decking to access the area.
Negative: adding more concrete adds more weight, not ideal on a hillside or if you have subsidence problems
Positive: Since the deck was built over the pad, it may have support members that rest on the concrete - so removing the concrete may mean adding some piles or footers for the deck, or trying to demolish all but some small pillars of concrete (which sounds difficult!)
And you'll need to backfill the area where the concrete was anyway, else its going to pond rainwater there.
Or leave it all as-is and simply add a roof over this deck. This minimises rain water, but may not be suitable for your particular situation.