How do I repair drywall behind kitchen tap?




We have water damage on the two foot by five inch high bit of drywall that is beneath the kitchen window, and behind the tap. It's from seven people, over time, splashing water. The drywall seems to be rotting and there is mold. I really don't want to cut it out and try to get a new piece to fit. Can I just use a good mold paint to cover over it and put a back splash on top? Will the paint keep the mold from continuing to spread?
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No such thing as mold paint it needs cut out removed and the area treated with mold killer, need to check the studs and frame of cabinets & surrounding area of sink & wall under sink; if you can see the mold there is alot more than you think. you need to replace drywall with water proof cement backer board and replace any moldy studs,framing, wood with special treated mold proof lumber;we had water leak did not even see any mold yet there was so much in walls,studs,framing it was about 12,000.00 damage total(and I live in AZ wg here it's dry) then you can prime & paint it. If you don't get it all removed & treated it will not go away and eventually spread.
You will need to cut out and replace.
Mold is mold, needs to be addressed or it will become a bigger, more expensive and inconvenient problem. Fix it now before it gets out of hand and the haz mat guys need to come in.