You can think of piss as one plain, rough word for the body letting liquid out, and for that liquid itself. Almost everything else the word does grows from two things in that picture. First, the liquid comes fast and freely and is hard to hold in. Second, it is the thing nobody wants. Rain that pours down, laughter you cannot stop, a drink that is not worth drinking, a person you are putting under you — the same picture is doing the work each time. The word also carries its own roughness. Saying it is a small act of choosing not to be polite, which is why so many of these uses live in jokes, insults and complaints.
From the word’s history
Wiktionary traces piss to Middle English pisse and pissen, from Old French pissier, possibly from Vulgar Latin *pissiare, and says the root is probably imitative — the word copies the sound of the liquid. It pushed out the older English words micge (urine) and migan (to urinate).
Wiktionary 記這個字來自中古英語 pisse／pissen，再往上是古法語 pissier，可能出自通俗拉丁語 *pīssiāre。它多半是個擬聲字，也就是照著水聲造出來的。它後來取代了古英語的 miċġe（尿）和 mīgan（撒尿）。名詞和動詞一開始就是一組，所以今天兩邊都有一整排用法。
Wiktionary, "piss"
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