Do I need to render a salute to an officer when my hands are occupied?

Could you have held both for a second with your left arm? Binder under arm and mug on hand.

I’ve dropped stuff before to salute someone, or walked far far away

no . stand or sit at attention . basic instruction . csm is abusing power . but then cup in hand may be construed as out of uniform (stretching it) .

Yes

Funny story...
While at OCS they have their own set of OCS Land Rules you follow. So one day showing up to the Barracks I was carrying a ton of crap and out of nowhere a TAC Officer walks around the corner, I easily could’ve gotten away with announcing The First Five Words with the proper greeting of the day since I had a ton of stuff on my back and in my hands. But being the jackass inside I just threw all my shit to the ground and screamed the First Five Words and proper greeting of the day with a salute and that TAC Officer stopped and couldn’t stop laughing while saluting me back. Then he told me to get the hell outta of there! He never messed with me again throughout OCS, I guess he knew That I knew how to play games too. Haha

I don’t know if anyone else already threw this idea out there, but maybe take and use a lesson from the E-4 mafia on this one and create a new option. Provided there are no regs prohibiting, invest in an in-reg courier bag and sling that shit over your shoulder. If you’re running binders/folders/paperwork back and forth between buildings all day, it might be reassuring to know you aren’t going to lose anything accidentally to wind/water/carelessness. And frees up your left hand for your mug. Right hand is free, so render salute and carry on smartly about your day, amirite?

In that situation (during my 22 years of service) I would try to hold the binder under my left arm so I could then hold the mug in my left hand, which would enable me to salute. Not for the whole walk, mind you, just when I saw the officer approaching. Return to holding things normally after you've passed him/her. Or the alternative is that when you see them approaching, you turn and walk a different direction temporarily in order to not pass within saluting distance. LOL. Yes, you are technically correct that if your hands are full, you don't need to salute- but it never, ever feels right doing it.

Need to clear Right Hand / Arm to the Left Hand / Arm to render the greeting if possible unless you can't discard your load. There is two alternatives. You can sit your load down and render the greeting or the Officer says "Carry One".

Only an officer who is a real dick would make a big deal of this. In Vietnam, in the field, officers didn't want to be saluted because snipers liked to target officers.

Unless what you are carrying requires 2 hands your right hand should never be full. A binder and a mug is incorrect and your failure to render a proper salute is all one you.

My experience, as a CW3, was to use common sense. If I approached someone obligated to salute but, legitimately, had his hand full, I returned the salute he was going render.