In BSE/NSE listed stocks how do they classify stocks into large, mid or small cap or blue-chip stock ??

First know what do you mean by 'Cap ' in Mid cap or Small cap.
Cap stands for Market Capitalization

Market Capitalization = Current Market price per share * no of shares outstanding.

So basically there is a maket capitaization range for each of the category : LARGE cap
MID cap and
SMALL cap
So if the company's Market Capitalization falls under that range then accordingly NSE /BSE categorizes that stock in the MID cap or SMALL cap etc

For Example consider the CNX Midcap 200 index :

For inclusion in the index, the average market capitalisation of a company must range between Rs.0.75 billion to Rs.7.5 billion.