When installing drywall around the main electrical panel should I take off the panel cover and then reinstall the cover after the drywall is in place? Is switching off the main breaker all I need to do as a precaution?

If the cover is a flange type, in other words extended to cover the wall finish, then you would need to remove the cover.

Shutting of the Main Breaker is definitely required.

If the Main breaker is in that panel, there will still be live conductors that feed the Main Breaker and extreme caution will be needed.

Follup- is there somewhere else to disconnect the power, outside, maybe?

Maybe, depends on what you have. Many homes just have a meter showing, no box to open. Post a picture and we could tell better. Like TK said the open panel will still have power but just don't stick fingers or screw drivers in there.

No worries, I don't plan on "poking around" inside the panel while the cover is off. I just wanted to make sure I wasn't missing something. Thanks for the quick answers!!

As an Electrician, I leave the cover off, and cut a piece of cardboard same size as inside of panel, push inside the outer lip, and maybe a couple pieces of fir strips sideways to hold in
Place. Protects the breakers, and painter won't get paint on the buss.
It is easier to keep clean than it is to clean it.

I assume that you are framing and drywall around a surface mounted circuit breaker panel. I suggest that you frame around it, leaving about 6" on each side and the top and bottom. Then build a cover for that opening. You might want to get into that panel to do some wiring one day.

I was thinking this was inwall, if so, stub spare conduits out of top and bottom.