This is a term used when someone turns red (blushes) because they are embarrassed.
A beet is a red "food source," so when people say red as a beet, they mean the person is either really embarrassed (blushing) or something to that affect.
got angry
This is not an idiom. When you see AS ___ AS ___, you are looking at A Simile. This one is comparing something to the red color of a turkey's wattle.
Radish
A homophone for a red vegetable is "beet" which sounds like "beat."
The common name for a beet is a red beet or simply a beet.
The homophone for beat is beet. Example sentence: A beet is a purplish, red root vegetable.
In debt. Its antithesis, "in the black," refers to having a balanced budget.
Beet juice.
The color of the herring in the idiom "-herring" is red.
It means to be patriotic (by reference to flying the flag).
A homophone for "red vegetable" would be "beet," and a homophone for "thrash" would be "thresh."