“Mining” as opposed to “minting” w.r.t. Bitcoin and other cryptocurrencies
"Mining" is apparently the established term for bitcoin, which seems to have been influential on following cryptocurrencies (I don't know much about the history of cryptocurrencies, so I can't give a detailed account). Satoshi Nakamoto's paper "Bitcoin: A Peer-to-Peer Electronic Cash System" includes the analogy to mining:
The steady addition of a constant of amount of new coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and electricity that is expended.
(§6 "Incentive", p. 4)
This model is opposed to a model involving a (metaphorical) "mint", which Nakamoto describes as involving a centralized authority:
A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank.
(§2 "Transactions", p. 2)
This may be a reason why the word "minting" was felt to be inappropriate to describe the generation of decentralized cryptocurrencies such as bitcoin.