The grand jury is separate from the court, but since Mueller empaneled the GJ if he is successfully fired by Trump/DOJ I assume it would be dissolved since the investigation per se is shut down.
I don't think that's true. The grand jury system is largely a legal abomination. It typically serves as a way for a prosecutor to clear or indict an individual at will, without having to take personal responsibility for that outcome.
It's commonly said that a prosecutor can get a jury to "indict a ham sandwich." The opposite outcome can typically also be assured.
However, in principle, the grand jury is its own boss, and has very broad discretion about how to proceed. In theory, the prosecutor follows the grand jury's instructions. In practice, the members are usually relatively clueless ordinary citizens who follow the prosecutor's lead.
If Mueller were fired, another prosecutor would have to take over. I'm pretty sure nobody has the authority to cancel a grand jury, once empaneled.
I don't think Mueller would take this step unless he intended the outcome to be indictments. Obvious charges would be conspiracy to violate campaign finance laws, obstruction of justice, and RICO charges.
I think Trump may have only two ways out: either get Mueller replaced with someone who will guide the grand jury away from issuing indictments, or issue pardons for anyone who might be targeted, including himself.
He's outraged enough senators already so that either course of action would likely lead to impeachment. His best strategy to save himself might be to issue pardons right away, before his level of support in the Senate drops lower.
As I think Buddy has pointed out, Trump seems to be decompensating as pressure mounts. I suspect he may get suspended by Cabinet vote prior to impeachment proceedings. Whether that happens before he tries to issue pardons is anyone's guess.