Is a 2000 penny that has been struck off-center cutting part of the In God We Trust off worth anything?

You have what's called an off-center strike. It happens when a coin blank (called a planchet) doesn't center properly in the collar that's supposed to hold it for striking. The die hits off to one side, so the image is skewed. Off-center cents are fairly common since so many coins are struck each year. A recent coin like yours would probably retail for about $2. Of course a dealer would pay even less, so it might be worth either just holding onto it as a conversation piece or trading for something you find more attractive. Don't write off all off-center coins, though. Some older error coins like buffalo nickels, or larger ones like half-dollars, can be worth as much as a couple of hundred dollars, depending on how off-center the strike is.