As a UE citizen with American B1/B2 visa I have 10 h layover in NY before I travel to Rio. Is it possible to leave an airport after I arrive from Europe and then check in again after layover?
it's unclear if you're asking if you are allowed to (visa rules) or if it's worth doing / do you have enough time with ten hours titularly. Assuming you mean "is it worth doing..."
If you are happy to just take a taxi both ways (and it's not a problematic traffic time of day), I'd say yeah just go straight in to Manhattan. I'd choose ahead of time a typical Manhattan restaurant; go straight there, see the skyline on the way in, have a meal, relax, walk around a little, and go straight back to your Rio flight.
I wouldn't be complicated in choosing a restaurant, just have lunch at The Plaza or the like, so you see the main areas from the taxi ride (Central Park, etc). If you try to choose some insider hip place or whatever, the timing will work against you or it will be full, etc.
Conversely if you ate enough on the plane, and prefer to stretch your legs just go to MOMA.
That's about what you have time for (again, just keep an eye on road traffic),
If you have not been to NYC before, note that if you're from Dubai (your question has a typo, as mentioned in the comments), it's probably rather pointless going "in to Manhattan". You'll just see an ancient, amazingly tedious, version of "big city", you presently live in one of today's actual "big cities" so there's not much point.
(I.E., you'll get to see things as thrillingly exciting as "branches of The Gap". Regarding say "large buildings", if you're from Mumbai, Shanghai, Dubai or whatever you won't notice any. Regarding "culture", ok you can drive around downtown for 5 minutes and see where Blondie came from back in the last century, while observing the other branches of "The Gap".)