Literally it means to cut something until it falls down, like a tree, so figuratively it means to "fell" someone, usually with a sarcastic or "cutting" remark.
Teach you a lesson.It means to deflate your ego, to humble you in front of your peers.
To do work and focus
Distill down, or boil down, as an idiom, means to get to the essence of something, or to simplify it.
Someone did something to jeopardize your standing. Other variables-took the ground away beneath your feet, cut you down to size, etc. etc.
I've never heard that idiom before. Perhaps you mean DOWN AND OUT, which means that the person is at a low point in their life, that they're poor in every way and not likely to make a success at anything in the near future.
sit down come over to
The idiom "feeling down in the mouth" means feeling sad or unhappy. It refers to someone looking sorrowful or melancholic, with their mouth turned downwards indicating their emotional state.
To be cut down to size is to be humbled.
This is an idiom meaning to narrow your focus down. It can also mean to narrow your aim and focus on one thing to hit. Picture the zero as a target and you get the idea of the idiom.
Yes.
Cut; to cut down
"Cutting" a deal just means making one. You're compromising, or making an agreement. "Cut" is used in the sense of stamping out or creating.