In simple terms no, a NFT Non-Fungible Token is not mined but rather minted.
Mining is a reference to cryptocurrency made famous by Bitcoin. Bitcoin is a cryptocurrency that people can mine via processing advanced algorithmic calculations on the blockchain. Mining for bitcoin is basically churning through blocks of data and when you have finished processing you are rewarded with some bitcoin.
The blockchain is the main database of cryptocurrency and NFT also sits on the blockchain. It is essentially the core database; it has every transaction listed and stored for public viewing. That's right the blockchain is publicly accessible for anyone with a web browser.
So mining is more relevant to searching for coins on a blockchain. Nowadays mining requires specialised equipment using ASIC processors designed for mining. The expense is high and electricity usage is a global concern as mining farms consume a great deal of electricity to feed the farm and keep it cool.
NFT is minted, minting is essentially creating like saving a file on your computer your file does not exist until it is saved. In the same way an image is just an image until it is saved in a Non-fungible token NFT wrapper on a blockchain.