Sarcasm has an element of two-facedness; you say one thing but mean the opposite. It's best served with a dash of humour, a pinch of bitterness, or a dollop of diss. We don't want to confuse it with exasperation, trolling or passive-aggressiveness (though I suppose there is some intersection with the latter).
A sarcasm emoji would be the emoticon equivalent of writing the word "NOT" immediately after a statement. Here's an example:
"Are you hurt?"
"I'm fine! I always scrape my face on the pavement like this to keep my complexion glowing. NOT."Or you can use the emoji like this:
"Shall I call 911?"
Here's the cut & paste markdown:
Some folks must think I just pull this stuff out of my behind. But it's fine. I enjoy staying up until 4 AM doing drawings for other people. Really.