If you hear a nice paradox like "this sentence is wrong" for the first time, you think "well, if this sentence is correct, then it is wrong because that's what it says". Then you think "But if the sentence is wrong then it is correct". (You can argue this two different ways: If the sentence is wrong, then its statement "this sentence is wrong" agrees with reality, so the sentence is correct. The other way: If the sentence is wrong that means it's statement "this sentence is wrong" is wrong. Since "this sentence is wrong" is wrong, the opposite "this sentence is correct" is correct).
Now you can start with the same argument again. But you are not going to do this infinitely, because one of two things happen: Either you figure out that after two steps of the argument you come back to the original, so you end up saying: "'This sentence is wrong' is a very strange sentence, because whether I assume it's right or wrong, I always conclude the opposite". Or you don't figure it out, but you get bored with the whole situation, and you say "This is too difficult for me, I've had enough of it, I'll think about something else".
Anyone trying to create a high-powered artificial intelligence would be aware of this and make sure that in difficult cases the AI doesn't get stuck in an infinite loop but either detects that there is a loop, or just gives up. Same as a human would do. So asking such an AI "is the sentence 'this sentence is wrong' right or wrong" wouldn't result in a smoking pile of metal containing a former AI, it would result in a quick answer "This is a paradox, because whatever I assume leads to the opposite" or a slower answer "I thought about it very hard for five seconds, and I can't figure it out".
(What would be hard is to decide when the AI should give up. This sentence looks easy enough, so you could think that if the AI can't figure it out in five seconds, it never will. But if you ask an AI to figure out a way to solve the problem of food supplies in third world countries, that's a hard problem, where finding a solution is expected to take a long time, so the AI should be allowed or allow itself to think about it for a very long time).