내 농담에 완전 갑분싸 됐어

The line, explained

You tell a joke. Nobody laughs. The silence has a temperature. Korean has a three-syllable word for that drop in temperature, and once you know it you will see it printed across half the variety shows you watch. 갑분싸 is slang, but using it well needs a feel for Korean social physics: who caused the chill, how it is named afterwards, and how a self-aware confession like today's line helps everyone move on. Let's break the sentence down and then the word.

내 농담에 is 내, 'my', 농담, 'joke', and 에. The particle here is causal as much as locative: 'at my joke, because of my joke'. 완전 is the casual intensifier Koreans use constantly, a clipped 완전히 that means 'totally'. 됐어 is 되다, 'to become', in the past: 'it became'. So the skeleton is 'at my joke, it totally became X', and X is the mood-kill itself. Note the subject is the room, not the speaker; Korean lets the atmosphere do the becoming.

갑분싸 is built from a full sentence. 갑자기 is 'suddenly', 분위기 is 'atmosphere, mood', and 싸해지다 is 'to go cold', from 싸하다, the adjective for a cold tingling feeling, the chill you get from menthol or from dread. Take the first syllable of each, 갑, 분, 싸, and you have the word. Koreans compress phrases this way all the time, 아아 for 아이스 아메리카노, 현타 for 현실 자각 타임, and understanding the habit unlocks dozens of words at once.

Grammatically 갑분싸 behaves like a noun for a state. The room 됐어, became it. A person 만들었어, made it. You will also hear 갑분싸 시키다, 'to cause 갑분싸', and 갑분싸 분위기 as a modifier. It is firmly casual and firmly online in flavour, so it belongs in group chats, captions and conversations with friends, not in anything your boss reads. For a neutral version say 분위기가 싸해졌어 or 분위기가 어색해졌어 (the mood got awkward).

Swap the cause and the confession keeps its shape: 내 질문에 (my question), 내 고백에 (my confession, which in a drama is the classic trigger), 내 실수에 (my slip-up), 내 한마디에 (my one remark). The point of saying it yourself is that it works as repair; naming the chill is the first step to breaking it. So the next time a Korean friend's eyes widen after something you said, beat them to it: 아, 갑분싸. They will laugh, and the temperature will come back up.