How are cryptocurrencies reported in GDP? Apparently the total market value of cryptocurrencies is currently close to $118 billion.

Is any of this reflected in GDP figures over the years? For example, if I start mining bitcoin today, I will consume electricity and produce bitcoins. How does this affect GDP?
Mining cryptocurrency can be considered an export of computing processing time, which is paid in a foreign currency (e.g. BitCoin).

The GDP is a measure of production of wealth of a nation. Exports and imports are considered in every method of calculating the GDP. You can read more on how each country calculates their GDP in this Economist article.

It is important to note that the actual GDP for each country is an estimate: it is very hard to calculate accurately the GDP, as you can imagine it is hard to calculate all of the consumption information about a given economy (cash transactions, informal markets, etc.). 
However, economists try to include every single expenditure via estimations: the UK includes estimates of drug sales and prostitution as an illustration of the attempts to be accurate. I believe cryptocurrencies could fall in the same category.

Additional reading on the guesstimates of the GDP here.