Intentionally throwing food off of the tray is not something I ever experienced with Brayden. Sure, food fell off the tray while he was eating sometimes, but he never intentionally threw it off.
Then Kaitlyn came along. She is such an easy baby in so many ways, but she does have her vices. One of those is dropping food off her tray. I wasn't sure she was doing it on purpose at first, but after some observation, I came to realize she was.
She doesn't do it immediately; she signs and says "all done" first, but if I don't respond fast enough and she is feeling impatient, she starts to throw her food on the floor. I am pretty sure she has learned that I quickly respond when she throws her food. The problem here is that with two kids, I can't always immediately respond to the desires of one, so when she is done, I can't always get her out right away. Another problem I have is that she is trying to get my attention in the appropriate and polite way first, then moving on to other means.
My personal solution for this mostly lies with myself. I have made more of an effort to respond to her as soon as she asks in her appropriate way. If I can't get to her right away, I at least look at her and tell her I will be there in one minute. She is less prone to throw food if I at least acknowledge her.
If she announces that she is all done but I want her to stay in her highchair for a bit longer for whatever reason, I will immediately remove her food from her so she can't resort to dropping her food off her tray if she gets impatient.
But maybe your child is throwing/dropping without using better means of communication first. If that is the case, I would use the firm voice, "that's a no," 'mommy glare,' and then take the food away and tell her she can get out when she signs or says all done, not by throwing her food. If your child is old enough to be sitting and eating finger foods, then she is most likely old enough to communicate in some way that she is done (other than throwing food).
The first couple of meals, I would take her hands and physically sign all done for her and also say it. I would then tell her good girl and get her out. After a few times (based on age and ability), have her do it herself. When she does it, praise her for being a good girl and obeying, etc.
If you are sure your baby just can't communicate that yet, then I would say you need to watch more closely for other cues. You want to catch her before she gets to the food-throwing point. Get her out before that point. Before you get her out, ask if she is all done and sign it to her and/or for her.
What you don't want to do is have baby throw food because she wants out and you then immediately get her out. That is reinforcing the wrong behavior. That is the reason I suggest you remove the food, then have her sit and ask nicely.
If your baby is throwing food just randomly throughout the meal, then you can take the food away immediately and wait for 30 seconds to a minute. Then give it back to her and tell her she can have her food but may not throw it. At some point (up to you) you would take it away for good. You could also take her out of the highchair and tell her she can go back if she will not throw her food.
Don't underestimate the comprehension ability of your children. They understand much earlier than we realize, and much earlier than they can really show their comprehension.
See also this post:
Baby Highchair Manners: http://babywisemom.blogspot.com/2008/02/baby-highchair-manners.html