Australian mining engineer here. Australia has government mandated environmental reports, rehabilitation requirements, aboriginal archeological surveying and protection, indigenous community negotiations and employment and industry standards (like the JORC code) for reporting to the market.
Presently there is no government with jurisdiction outside of Earth, but we can still expect some industry standards and corporate policies to be in place.
Number one is a standardised system of ore reserving (Google JORC Code for examples). If you are mining asteroids, for instance, investors need a minimum level of confidence in the geological knowledge and technical and economic challenges of retrieving the ore. Exploration drilling provides the initial information that gives investors the confidence to back your mining project.
Before drilling you will have to define a lease boundary (ie. Asteroid 52B) and establish your theoretical legal right to mine. Even if there is no government regulation, your legal team will still want the papers ready for the inevitable legal challenge. Example: Some government might try to nationalise your company, or a competitor may infringe on your lease.
Environmental and cultural obligations will grow out of the first landmark court cases. For instance, the moon is a sacred heritage site to all humans. There will undoubtedly be a ruling that no mining activities shall be visible to the naked eye on Earth. Expect to see that tick box in a report somewhere - worth noting simply for the sheer bureaucratic absurdity of ticking it off for every comet in the Oort.
As for bio-contamination and extra-terrestrial life... short answer is, no one will take it seriously. The long answer is that space is BIG, and no one is going to send Mines Inspectors halfway across the solar system to check whether there are green tree frogs on Ceres. You pretty much have your bases covered by randomly sampling the exploration cores for microbes, and leaving a webcam running to detect little green men. This will be included in your quarterly Environmental Disturbance Report.
Lastly, send non-confidential geoscience reports to NASA or some other industry body. Even though this might not be legally necessary, most long-sighted mining companies recognise the advantages of teaming up with academia for research and development purposes.
Never underestimate the amount of bureaucracy committed to corporate CYA, especially if the laws haven't been written yet.
Edit: if you are re-routing asteroids, add in a mandatory Orbit Change Request. It is both a traffic hazard and planetary impact threat.