These sentences are structurally correct, but they might be used if two people understood what "the grumpy face" specifically was.
A man might say to his wife, "Hey, don't give me the look!" meaning, there is a specific look she gives him that means a certain thing. So if someone says to me, "Don't give me the grumpy face" -- of course I know it's a grumpy face, but "the" meaning it's a certain grumpy face that between the two of us has an added meaning.
Same thing for "stop doing your grumpy face" or "stop doing that grumpy" face. It tells me that there is a certain grumpy face (if there's more than one) that I don't like, and wish they'd stop.
And for your last sentence, the better one is "Don't show any excitement" even though both are technically correct. It just sounds better.