Those are not Cutouts.
What you are looking at is the Angled Deck.

It allows the Navy to conduct simultaneous Launch and recovery operations.
Planes can be taking off on the Bow Cats (Blue Arrow) while other planes are landing on the angled deck (Red Arrow).
The reason the deck remains flared outwards aft of the Angled Deck and forward of the Island structure is because that is where the Elevators are that move the planes from the hangar deck to the flight deck.

What you think of as Cut ins, is just where the Deck isn’t flared outwards, giving MORE room, not taking away room.
OK, the primary answer that comes up, is only partially correct. A better way to explain why it has this particular shape, is looking directly down on the carrier to understand.

In the photo above, I placed a yellow line showing the landing strip on the carrier. The red lines represent the catapults where aircraft are launched into the air. Generally speaking, these operations don’t happen together. While it is possible, it becomes extremely dangerous to land aircraft while others are launching, so they do one launch period, then a recovery period.
Now the reason the landing strip is angled, is mainly for safety reasons. When aircraft come in for a landing, or trap, they need to have a clear path off the ship if they miss the wires that arrest their plane once they land on the carrier. The pilot push the throttle to full power when they land, so they have enough power to take off again, if they missed the wires, this is called a bolter.
When aircraft land successfully, they are immediately guided to the front of the ship, into the bottle neck, out of the way of the next plane making their landing. This is why they have separate times for launching, then recovery, it’s just too dangerous to do both at the same time. Plus, it would be incredibly inefficient.
So while it’s true it can do both, it isn’t done at the same time. The other thing to understand, both launching and recovery of aircraft is always done into the wind. When launching, the carrier runs straight into the wind, giving aircraft more lift as they launch into the air.
When recovery is ongoing, the carrier actually turns right constantly during a landing. This gentle right turn actually gives the pilot as straight a flight path onto the carrier deck as possible.
It is difficult to explain how that works. But imagine how much more difficult it would be for pilots if they had to guess where the landing strip would be, when they reach the carrier. This is what they would have to do, if the carrier remained on a straight path during landings.
If you look at the ship, then consider an aircraft flying direct at the back of the ship, they would not be able to land on the landing strip, unless they made a left turn right before their wheels hit the deck, that would be extremely dangerous.
So the carrier turns gently to the right(starboard), which effectively straightens out the landing strip as the pilots come in. Seems weird that in order to land straight, the carrier has to turn.
