... I'm assuming you could write off some potrion of your electric bill, your internet, mining rent space area (whether it be home or business), the equipment and whatever else might be able to be written off or deducted. I'm wondering if I could claim this as a home business and get enough deductions to offset the taxes I pay on my full time real day job?
Yes you can on a Form 1040 Schedule C subject to certain limitation, but the idea of claiming the mining expenses is to offset the mining income and hopefully have a profit. Hint: utilize §179 deduction to expense all of your initial hardware purchases in the year of purchase. If you are doing something for fun and not worried about losing money, you can't offset these "hobby losses" against your other income. Three years of straight losses and the IRS will assume that it is a hobby. However, the IRS will make you pay tax if you make money on the hobby.
We had to file that because her mystery shopping company sent her an income tax declatation for being an independent contractor (I can't remember the form number but like a W-2). Had she stayed under a $400 threshold that we did not know existed, it would have been free money. Instead, since she made over the $400 low limit they hit her with an independent contractor earnings tax fee of about 40% on her earnings.
It was a Form 1099 that your wife got. In her case if she made $399 it would still be taxable; the company just doesn't need to report the income to the IRS. Similarly, there is no such de minimis exception for mining income: you make $1 and the law requires your to pay income tax and self employment tax.