Unknown. One theory is that this is a native Japanese term, with the su reading somehow related to the way that very sour things cause one to pucker.
Given that vinegar was historically introduced to Japan in the 300-400s from China, another possibility is that the su reading is from Middle Chinese醋 (/t͡sʰuoH/) instead, with the 酢 spelling as an example of jukujikun (熟字訓), and that this su reading naturalized and came to be regarded as a native kun'yomi rather than a Chinese-derived on'yomi. Compare modern Mandarin醋 (cù) or Cantonese醋 (cou3).
酢が過ぎる (su ga sugiru): “vinegar is excessive, too much vinegar” → doing too much, being excessive
酢でさいて飲む (su de saite nomu): “cutting something with vinegar and swallowing it down” → in reference with the ease of cutting a fish, dipping it in vinegar, and eating it: doing something very simple
酢でも酒塩でも (su de mo sakashio de mo), 酢でも蒟蒻でも (su de mo konnyaku de mo): (used with a negative verb): “by vinegar or by cooking wine”, “by vinegar or by konjac” → something that cannot be done in the usual fashion, or cannot be done easily
酢に当て粉に当て (su ni ate ko ni ate), 酢につけ粉につけ (su ni tsuke ko ni tsuke): “with regard to vinegar and flour”, “about vinegar and flour” → about something, about various things; from time to time
酢にも粉にも (su ni mo ko ni mo), 酢にも塩にも (su ni mo shio ni mo]), 酢にも蛸にも (su ni mo tako ni mo), 酢にも味噌にも (su ni mo miso ni mo): “about/in vinegar and flour”, “about/in vinegar and salt”, “about/in vinegar and octopus”, “about/in vinegar and miso” → about anything, in anything
酢の粉の (su no ko no), 酢の蒟蒻の (su no konnyaku no): “of vinegar, of flour”, “of vinegar, of konjac” → of anything, belonging to anything
酢を買う (su o kau), 酢を乞う (su o kou): “to buy vinegar”, “to beg vinegar” → to lose goodwill through excessive sycophancy, to anger someone by saying more than one should; to agitate or instigate, to stir things up