So, if I mined through 2013 at an average price of say $200/btc and put my coins on gox, then lost them with gox's closure when the price was ~$500 then...
I pay income tax on the $200/btc mined coins - my mining equipment and electricity expenses
Can I then claim property loss at the price when gox closed?
You pay income tax on your $200/btc mined coins, and then you take a capital loss for the coins (again at $200/btc).
Alternatively you could declare a gain of $300 and then a loss of $500 but it would end up the same anyways as $300 of the loss would cancel out the gain.
Hopefully you had other capital gains that year you can cancel out because you can only deduct $3500 in capital loss off of your income per year (you can carry it over to future years though).
If you actually mined a lot of coins, never sold them, and then lost them all when gox went under you could actually end up owing more tax than money you have because of the inability to deduct your capital loss.