To mine Bitcoin as cheaply as possible, I think that India would be your best bet. I'm not saying that it will be profitable however.

Let's assume you want to mine Bitcoin. All you technically need is a place to live and keep your miners (house/apartment), an internet connection, and a low cost of living. 

Looking at a basic graph of electricity costs from 2011, India and China is by far the lowest.

Image source: https://www.ovoenergy.com

And in terms of cost of living and other expenses, they are one of the lowest in the world. Second best only to Pakistan according to the Cost of Living Indices found on Numbeo.

Here's a link if you're interested: https://www.numbeo.com/cost-of-living/rankings_by_country.jsp

So taking it all into consideration, India is my answer.