You have two different income streams to consider.
When you mine the coins, you have income on the day the coin is "created" in your account at that day's exchange value. You can report the income as a hobby or as self-employment. If you report as a hobby, you include the value of the coins as "other income" on line 21 of form 1040. Your ability to deduct any expenses is limited -- expenses are itemized deductions subject to the 2% rule.
If you report as self-employment income (you are doing "work" with the intent of earning a profit) then you report the income on schedule C. You can fully deduct your expenses (if you can prove them) (see later). The net profit is subject to income tax and self-employment tax.
Your second income stream comes when you actually sell the coins to someone else for dollars or other currency. Then you have a capital gain (if they were worth more when you sold them than when you mined them) or you have a capital loss (if they are worth less when you sell them). And the gain or loss will be taxed differently if it is a short term gain (you held it one year or less) or long term (more than one year). You will need to keep track of each coin you create (date, value) and when you sell it (date and value).
And of course, if you immediately sell the coin for cash, then you only have income from the creation, you don't also have a capital gain or loss.
Now, as far as expenses are concerned, if you are doing this as a schedule C business, you can take an expense deduction for computer equipment you buy (as depreciation, subject to all the rules) and your other expenses (mainly electricity, maybe a home office). But you need to be able to prove those expenses, such as with a separate electric meter or at least having your computer equipment plugged into a portable electric meter so you can tell how much of your electric bill was used in your business. Unless your expenses are very high, they won't offset the extra self-employment tax, so you will probably pay less tax if you report the income as hobby income and forget about the expenses. (On the other hand, if you report it as self-employment and pay SE tax, that adds to your credits in the social security system which may allow you to qualify for a higher retirement benefit. Having self-employment income on schedule C also allow you to claim some tax deductions like an IRA that you can't claim if all your income is hobby or "other" income. So there may be benefits to paying SE tax in the long run.)
If you earn more than a couple thousand dollars per year you will need to think about making estimated tax payments as well.
*Answers are correct to the best of my ability at the time of posting but do not constitute legal or tax advice.*
