1. To very quickly or discreetly depart (to some place), especially for a short length of time. I need to nip off to the store to get some milk—do we need anything else? I think they nipped off to get some more party supplies. They should be back soon.

2. To sever something (from something else) by pinching, cutting, or snipping it. In this usage, a noun or pronoun can be used between "nip" and "off." With great charm and grace, he bent down, nipped off a rose from the bush, and presented it to his date. Just let me get my scissors and nip these hairs off that the barber missed.