All is not lost if you end up paying the Social Security/Medicaid taxes from self-employment (due to making a profit of $400 or more). Half of it can be deducted from your income for income taxes. (The actual math is a bit complex.) Also, these are legit Social Security taxes, meaning you do get SS credits for paying them. This probably doesn't matter unless you don't have a job elsewhere. But hey, if you quit your job to work on bitmining full time, there you go.

If, as quite possible, your bitmining is unprofitable, you could theoretically use it to reduce your income taxes from another job or business. If you can convince the IRS it's not just a tax shelter disguised as a business. See: the hobby loss rule.

If you are planning to go into business as a bitminer, please research Section 179, since it will probably make your life much easier. Or, as Hive account@cryptotax says, consult a tax adviser on it.

Disclaimer: I'm not a tax professional, but I am a small businessman, so I learned this stuff.