Mining is Earned Income.
You can file a Schedule C as a business owner in which case you can claim expenses,
or
if you do it for fun, you might claim the income as Hobby Income. This way you can't claim a loss, but you also don't need to pay to file Schedule C and you won't pay Self-Employment tax.
Be aware that if you earn from Mining year after year, the IRS might insist you file Schedule C as a trade and pay Self-Employment tax on your earnings.
The main issue is do you do it for fun or profit?
Under Personal Income,
Scroll down to Miscellaneous Income at the bottom of the Less Common Income list
Click Start
Scroll down to Hobby income and expenses
You can click the blue "Learn More" link on that page for more information
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