In informal British English, someone who is half-cut has had too much alcohol. They are drunk, or clearly getting there — walking a bit loosely, talking a bit loudly. It does not mean they have been cut with a knife. You hear it about nights out, pubs, and parties. It is casual and a little teasing, not a doctor’s word, and not a kind word if the drinking is a real problem. Though actually, Americans almost never say this; they are more likely to say tipsy, drunk, or wasted. “Half-” here is not a careful measurement. Nobody is checking whether you are exactly fifty percent drunk.

喝醉了（英式口語，有點醉或明顯醉了）