...Fix the roof.
It's not complicated or mysterious - the roof leaks, so it's wet, and you need to stop that.
Which is going to be work if it's a concrete deck ( less if removable pavers so you can actually get to and replace the waterproofing under them. More if some optimist poured concrete over a waterproofing membrane that didn't last.) I see you have the latter case...
While it's easy enough to cut channels to remove puddles, that's not going to solve a clearly compromised waterproofing membrane under the deck surface.
At best guess you'll either need to demolish the concrete and repair the roof, or possibly grind it to solve the pooling and then build a new waterproof membrane on top of it, with a new traffic surface above that; assuming you still want to be able to walk on it.