It would be pretty easy to write a script, using the blockchain API to iterate all the mining receive transactions during the tax year on the receiving address(es) and to get a historical exchange values from the same API. The databases exist for free of charge, and you most likely have a computer that could run such a script.
please re-read my posts regarding the question remaining, how do you know which cashed out BTC, are from which exact mined BTC.
It helps zero to know, you received x btc at x price.
You need to know, that xyz bitcoin was recieved at xx price, and those same xyz bitcoin fraction was sold at yy price.
Your exchange keeps that information. If they are required to report it to the IRS, they will.
If you don't want to pay your taxes, then using poor record keeping isn't an excuse for not paying your taxes. Men with guns from the IRS can still come after you and demand payment of taxes using a worst case scenario (on your part) .
IRS agents don't carry guns.