Even if they don't sanction it, can they actually stop you from doing as you please with an asteroid Well they could fine you / put you in Jail here on earth.

Even if they don't sanction it, can they actually stop you from doing as you please with an asteroid Well they could fine you / put you in Jail here on earth. The state can't physically prevent you from murdering people in most cases, for example, but they can impose penalties when you do it. A commercial mining venture is unlikely to be successful if the government of its home country says what it is doing is illegal.