Those are ponds, so they will refill when it rains. Before that happens, you'll want to wall it off.
If you let the water spread out to 1/7 depth, it will evaporate over time leaving mud. You can get rid of the mud by building something and then demolishing it again. Or you can build a farm on the mud.
Or if you want to take advantage, dig a cistern near that breach, and then put a floodgate in rather than a wall.
If you (b)uild->(t)rap->(l)ever, you can then hook up the lever to the floodgate and turn the tap on and off.
(Don't put the water shutoff lever in the flooding zone tho!)
If you're in a rush to get the water out, or if you want to get it out of that channeled area in the south, you'll need a pump.
Manufacture a tube, a giant corkscrew and a Block, and assemble them into a screw pump.
Build the pump just above the water, and it can pump the water below it up to its own level.
You'll need a dwarf with the pump operator job enabled. Or you can build a windmill and link it to the pump with axles and gears.
It looks like you've got water spilling down the stairs in the east of the main room there. You could manufacture some hatch covers to prevent any more leakage, and then you'll have to either wait for evaporation, or build a bunch of pumps in a row/stack to get it all out.